Author: Carlos S. Kubrusly

Publisher: Springer

ISBN: 3319225065

Category: Mathematics

Page: 279

View: 5503

Classical in its approach, this textbook is thoughtfully designed and composed in two parts. Part I is meant for a one-semester beginning graduate course in measure theory, proposing an “abstract” approach to measure and integration, where the classical concrete cases of Lebesgue measure and Lebesgue integral are presented as an important particular case of general theory. Part II of the text is more advanced and is addressed to a more experienced reader. The material is designed to cover another one-semester graduate course subsequent to a first course, dealing with measure and integration in topological spaces. The final section of each chapter in Part I presents problems that are integral to each chapter, the majority of which consist of auxiliary results, extensions of the theory, examples, and counterexamples. Problems which are highly theoretical have accompanying hints. The last section of each chapter of Part II consists of Additional Propositions containing auxiliary and complementary results. The entire book contains collections of suggested readings at the end of each chapter in order to highlight alternate approaches, proofs, and routes toward additional results. With modest prerequisites, this text is intended to meet the needs of a contemporary course in measure theory for mathematics students and is also accessible to a wider student audience, namely those in statistics, economics, engineering, and physics. Part I may be also accessible to advanced undergraduates who fulfill the prerequisites which include an introductory course in analysis, linear algebra (Chapter 5 only), and elementary set theory.
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Author: Valeriy K. Zakharov,Timofey V. Rodionov,Alexander V. Mikhalev

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110550962

Category: Mathematics

Page: 478

View: 512

This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff’s classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff’s initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff’s classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz – Radon – Frechet problem of characterization of Radon integrals as linear functionals
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Author: Daniel W. Stroock

Publisher: Springer Science & Business Media

ISBN: 1461411351

Category: Mathematics

Page: 244

View: 6754

‘A Concise Introduction to the Theory of Integration’ was once a best-selling Birkhäuser title which published 3 editions. This manuscript is a substantial revision of the material. Chapter one now includes a section about the rate of convergence of Riemann sums. The second chapter now covers both Lebesgue and Bernoulli measures, whose relation to one another is discussed. The third chapter now includes a proof of Lebesgue's differential theorem for all monotone functions. This is a beautiful topic which is not often covered. The treatment of surface measure and the divergence theorem in the fifth chapter has been improved. Loose ends from the discussion of the Euler-MacLauren in Chapter I are tied together in Chapter seven. Chapter eight has been expanded to include a proof of Carathéory's method for constructing measures; his result is applied to the construction of Hausdorff measures. The new material is complemented by the addition of several new problems based on that material.
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Author: S. J. Taylor

Publisher: CUP Archive

ISBN: 9780521098045

Category: Mathematics

Page: 266

View: 5062

This paperback, gives a self-contained treatment of the theory of finite measures in general spaces at the undergraduate level.
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Author: Martin Brokate,Götz Kersting

Publisher: Springer-Verlag

ISBN: 303460646X

Category: Mathematics

Page: 160

View: 4472

Der Integralbegriff in seiner Ausprägung durch Henri Lebesgue ist ein grundlegendes Werkzeug in der modernen Analysis, Numerik und Stochastik. Für Lehrveranstaltungen zu diesen Gebieten der Mathematik bereiten die Autoren wesentliche Sachverhalte in kompakter Weise auf. Das Buch liefert Orientierung und Material für verschiedene Varianten zwei- oder vierstündiger Lehrveranstaltungen. In einem ergänzenden Abschnitt werden um den Begriff der Konvexität herum Verbünde zur Funktionalanalysis hergestellt.
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Author: Michael A. Proschan,Pamela A. Shaw

Publisher: CRC Press

ISBN: 1498704220

Category: Mathematics

Page: 328

View: 473

Essentials of Probability Theory for Statisticians provides graduate students with a rigorous treatment of probability theory, with an emphasis on results central to theoretical statistics. It presents classical probability theory motivated with illustrative examples in biostatistics, such as outlier tests, monitoring clinical trials, and using adaptive methods to make design changes based on accumulating data. The authors explain different methods of proofs and show how they are useful for establishing classic probability results. After building a foundation in probability, the text intersperses examples that make seemingly esoteric mathematical constructs more intuitive. These examples elucidate essential elements in definitions and conditions in theorems. In addition, counterexamples further clarify nuances in meaning and expose common fallacies in logic. This text encourages students in statistics and biostatistics to think carefully about probability. It gives them the rigorous foundation necessary to provide valid proofs and avoid paradoxes and nonsensical conclusions.
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A Survey of the Mathematical Theory

Author: John W. Lamperti

Publisher: John Wiley & Sons

ISBN: 1118150430

Category: Mathematics

Page: 189

View: 9784

The brand new edition of this classic text--with more exercises and easier to use than ever Like the first edition, this new version of Lamperti's classic text succeeds in making this fascinating area of mathematics accessible to readers who have limited knowledge of measure theory and only some familiarity with elementary probability. Streamlined for even greater clarity and with more exercises to help develop and reinforce skills, Probability is ideal for graduate and advanced undergraduate students--both in and out of the classroom. Probability covers: * Probability spaces, random variables, and other fundamental concepts * Laws of large numbers and random series, including the Law of the Iterated Logarithm * Characteristic functions, limiting distributions for sums and maxima, and the "Central Limit Problem" * The Brownian Motion process
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Author: John Bates Clark

Publisher: Ludwig von Mises Institute

ISBN: 1610166175

Category: Business & Economics

Page: 584

View: 8079

John Bates Clark was an American adherent of the marginalist school who engaged the Austrians and learned from them. He delivered many blows against the historical school in favor of the idea of pure theory. He was also a prominent advocate of free markets in a time when the economics profession was embracing Progressivist ideology. Clark contributed to laying the foundation of what would later become a distinctly American Austrian School. Mises himself regarded him as an outstanding economist, perhaps his favorite American economist.

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Author: Kiyosi Itō

Publisher: American Mathematical Soc.

ISBN: 9780821838983

Category: Mathematics

Page: 171

View: 2861

This English translation of a classic text by renowned Japanese mathematician Kiyosi Ito offers a unified account of additive processes, stationary processes and Markov processes. Translation adds important updates to the discussion. Lucid explanations reflect Ito's important contributions to knowledge on stochastic processes and other areas of probability theory.
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A Complete Self-Study Course for All Musicians

Author: Shelly Berg

Publisher: Alfred Music Publishing

ISBN: 9780739043851

Category: Music

Page: 148

View: 6000

Alfred's Essentials of Jazz Theory is designed for jazz enthusiasts and musicians who want to learn jazz concepts and terminology. To get the most out of this course, it is recommended that you have a good understanding of basic theory, such as the lessons in Books 1-3 of Alfred's Essentials of Music Theory. The book contains lessons with both written and music reading exercises and ear-training and listening are addressed through the included CDs. Each unit is complete with a review section. Playing and/or singing along with each example is encouraged throughout the book. The Self-Study Course includes lessons, a complete answer key to check your work, and three listening and ear-training CDs.
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Author: Jewgeni H. Dshalalow

Publisher: Springer Science & Business Media

ISBN: 1461459621

Category: Mathematics

Page: 748

View: 9574

Foundations of Abstract Analysis is the first of a two book series offered as the second (expanded) edition to the previously published text Real Analysis. It is written for a graduate-level course on real analysis and presented in a self-contained way suitable both for classroom use and for self-study. While this book carries the rigor of advanced modern analysis texts, it elaborates the material in much greater details and therefore fills a gap between introductory level texts (with topics developed in Euclidean spaces) and advanced level texts (exclusively dealing with abstract spaces) making it accessible for a much wider interested audience. To relieve the reader of the potential overload of new words, definitions, and concepts, the book (in its unique feature) provides lists of new terms at the end of each section, in a chronological order. Difficult to understand abstract notions are preceded by informal discussions and blueprints followed by thorough details and supported by examples and figures. To further reinforce the text, hints and solutions to almost a half of more than 580 problems are provided at the end of the book, still leaving ample exercises for assignments. This volume covers topics in point-set topology and measure and integration. Prerequisites include advanced calculus, linear algebra, complex variables, and calculus based probability.
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Author: Andrew Surmani,Alfred Publishing,Karen Farnum Surmani,Morton Manus

Publisher: Alfred Music Publishing

ISBN: 9780739045480

Category: Music

Page: 124

View: 9551

Alfreds Essentials of Music Theory is designed for students of any age, whether listeners or performers, who want to have a better understanding of the language of music. In this all-in-one theory course, you will learn the essentials of music through concise lessons, practice your music reading and writing skills in the exercises, improve your listening skills with the available ear-training CDs (included with this item), and test your knowledge with a review that completes each unit.This Alto Clef edition includes primarily alto clef examples, but also presents treble and bass clef examples. The Student Complete Book includes Books 1-3 in a spiral-bound format.Book 1 (Lessons 1-25): Staff, Notes and PitchesTreble & Bass ClefsGrad Staff & Ledger LinesNote ValuesMeasure, Bar Line and Double Bar2/4, 3/4 & 4/4 Time SignaturesWhole, Half & Quarter Notes/RestsDotted Half & Quarter NotesTies & SlursRepeat Sign, 1st & 2nd Endings
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Author: Heinz Bauer

Publisher: Academic Pr

ISBN: N.A

Category: Mathematics

Page: 460

View: 4738

Measure and integration theory; Probability theory; Continuation of measure and integration theory; Further development of probability theory.
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Author: Karen Farnum Surmani,Andrew Surmani,Morton Manus

Publisher: Alfred Music Publishing

ISBN: 9780739002629

Category: Music

Page: 44

View: 1620

Alfred's Essentials of Music Theory is designed for students of any age, whether listeners or performers, who want to have a better understanding of the language of music. In this all-in-one theory course, you will learn the essentials of music through concise lessons, practice your music reading and writing skills in the exercises, improve your listening skills with the available ear-training CDs (sold separately), and test your knowledge with a review that completes each unit. Computer software is also available with randomized drilling of the material and scorekeeping. This Alto Clef edition includes primarily alto clef examples, but also presents treble and bass clef examples. Book 1 (Lessons 1-25): Staff, Notes and Pitches * Treble & Bass Clefs * Grad Staff & Ledger Lines * Note Values * Measure, Bar Line and Double Bar * 2/4, 3/4 & 4/4 Time Signatures * Whole, Half & Quarter Notes/Rests * Dotted Half & Quarter Notes * Ties & Slurs * Repeat Sign, 1st & 2nd Endings * Eighth Notes & Rests * Dynamic Signs, Tempo Marks & Articulation * D.C., D.S., Coda & Fine * Flats, Sharps & Naturals * Whole & Half Step, Enharmonic Notes. The complete line of Alfred's Essentials of Music Theory includes Student Books, a Teacher's Answer Key, Ear-Training CDs, Double Bingo games, Flash Cards, Reproducible Teacher's Activity Kits, and interactive software for students and teachers in private study, studio and network environments.
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Author: Andrew Surmani,Karen Farnum Surmani,Morton Manus

Publisher: Alfred Music Publishing

ISBN: 9780739044308

Category: Music

Page: 96

View: 5122

Alfred's Essentials of Music Theory is designed for students of any age, whether listeners or performers, who want to have a better understanding of the language of music. In this all-in-one theory course, you will learn the essentials of music through concise lessons, practice your music reading and writing skills in the exercises, improve your listening skills with the available ear-training CDs (sold separately), and test your knowledge with a review that completes each unit. The Teacher's Activity Kit for Volume 3 includes five reproducible activities for each of the six units in Volume 3 of the Student Books. The wide variety of activities includes Music Crossword Puzzles, Note Naming, Matching Games, Musical Math, Word Scrambles, and others for a total of 30 Activities in all. There is also one Test per Unit that covers all the theory concepts introduced in that Unit. Each reproducible page includes scoring boxes to help the instructor grade the page. The complete line of Alfred's Essentials of Music Theory includes Student Books, a Teacher's Answer Key, Ear-Training CDs, Double Bingo games, Flash Cards, Reproducible Teacher's Activity Kits, and interactive software for students and teachers in private study, studio and network environments.
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Author: Lawrence Craig Evans,Ronald F. Gariepy

Publisher: CRC Press

ISBN: 9780849371578

Category: Science

Page: 288

View: 8134

This book provides a detailed examination of the central assertions of measure theory in n-dimensional Euclidean space and emphasizes the roles of Hausdorff measure and the capacity in characterizing the fine properties of sets and functions. Topics covered include a quick review of abstract measure theory, theorems and differentiation in Mn, lower Hausdorff measures, area and coarea formulas for Lipschitz mappings and related change-of-variable formulas, and Sobolev functions and functions of bounded variation. The text provides complete proofs of many key results omitted from other books, including Besicovitch's Covering Theorem, Rademacher's Theorem (on the differentiability a.e. of Lipschitz functions), the Area and Coarea Formulas, the precise structure of Sobolev and BV functions, the precise structure of sets of finite perimeter, and Alexandro's Theorem (on the twice differentiability a.e. of convex functions). Topics are carefully selected and the proofs succinct, but complete, which makes this book ideal reading for applied mathematicians and graduate students in applied mathematics.
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Lessons, Ear Training, Workbook

Author: Andrew Surmani,Karen Farnum Surmani,Morton Manus

Publisher: Alfred Music Publishing

ISBN: 9780882849515

Category: Music

Page: 120

View: 6672

Alfred's Essentials of Music Theory is designed for students of any age, whether listeners or performers, who want to have a better understanding of the language of music. In this all-in-one theory course, you will learn the essentials of music through concise lessons, practice your music reading and writing skills in the exercises, improve your listening skills with the available ear-training CDs (included), and test your knowledge with a review that completes each unit. The Student Complete Book includes Books 1-3 in a spiral-bound format. Book 1 (Lessons 1-25): Staff, Notes and Pitches * Treble & Bass Clefs * Grand Staff & Ledger Lines * Note Values * Measure, Bar Line and Double Bar * 2/4, 3/4 & 4/4 Time Signatures * Whole, Half & Quarter Notes/Rests * Dotted Half & Quarter Notes * Ties & Slurs * Repeat Sign, 1st & 2nd Endings * Eighth Notes & Rests * Dynamic Signs, Tempo Marks & Articulation * D.C., D.S., Coda & Fine * Flats, Sharps & Naturals * Whole & Half Step, Enharmonic Notes. Book 2 (Lessons 25-50): Tetrachords & Major Scales * Key Signatures * Chromatic Scale * Intervals, Circle of Fifths * Perfect, Major & Minor Intervals * Augmented & Diminished Intervals * Solf�ge & Transposition * Sixteenth Notes & Rests * Dotted Eighth Notes & Eighth Note Triplets * Common Time & Cut Time * 3/8 & 6/8 Time Signatures * Pick-up Notes & Syncopation * Primary & Major Triads * Scale Degree Names * Dominant 7th Chord. Book 3 (Lessons 51-75): 1st & 2nd Inversions of Triads * Inversions of V7 Chords * Figured Bass * Major Chord Progressions * Minor Scales, Minor Triads * Augmented & Diminished Triads * Primary Triads in Minor Keys * Minor Chord Progressions * Modes * Harmonizing a Melody in Major and Minor Keys * Broken Chords & Arpeggiated Accompaniments * Passing and Neighboring Tones * Composing a Melody in Major and Minor Keys * 12-Bar Blues Chord Progression & Blues Scale * Basic Forms of Music. The complete line of Alf
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Author: G. A. Young,R. L. Smith,R. L. (University of North Carolina Smith, Chapel Hill)

Publisher: Cambridge University Press

ISBN: 9780521839716

Category: Mathematics

Page: 225

View: 8521

Concise account of main approaches; first textbook to synthesize modern computation with basic theory.
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Author: John Billingsley

Publisher: CRC Press

ISBN: 1420091247

Category: Technology & Engineering

Page: 339

View: 6027

Carefully separating the essential from the ornamental, Essentials of Control Techniques and Theory presents the nuts and bolts for designing a successful controller. It discusses the theory required to support the art of designing a working controller as well as the various aspects to convince a client, employer, or examiner of your expertise. A Compelling Account of the Basics of Control Theory Control solutions for practicing engineers Using the author’s own Javascript On-Line Learning Interactive Environment for Simulation (Jollies), the text relies on computer-based graphical analysis methods, such as Nyquist, Nichols, root locus, and phase-plane, to illustrate how useful computer simulation can be for analyzing both linear and nonlinear systems. It explains step-by-step the design and modeling of various control systems, including discrete time systems and an inverted pendulum. Along with offering many web-based simulations, the book shows how mathematics, such as vectors, matrices, and the differential equations that govern state variables, can help us understand the concepts that underpin the controller’s effects. From frequency domain analysis to time-domain state-space representation, this book covers many aspects of classical and modern control theory. It presents important methods for designing and analyzing linear systems and controllers.
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Author: Richard Durrett

Publisher: Springer Science & Business Media

ISBN: 146143615X

Category: Mathematics

Page: 266

View: 9916

This book is for a first course in stochastic processes taken by undergraduates or master’s students who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and mathematical finance. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding The book has undergone a thorough revision since the first edition. There are many new examples and problems with solutions that use the TI-83 to eliminate the tedious details of solving linear equations by hand. Some material that was too advanced for the level has been eliminated while the treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved. For example, the difficult subject of martingales is delayed until its usefulness can be seen in the treatment of mathematical finance. Richard Durrett received his Ph.D. in Operations Research from Stanford in 1976. He taught at the UCLA math department for nine years and at Cornell for twenty-five before moving to Duke in 2010. He is the author of 8 books and almost 200 journal articles, and has supervised more that 40 Ph.D. students. Most of his current research concerns the applications of probability to biology: ecology, genetics, and most recently cancer.
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