Lebesgue Measure and Integration

An Introduction

AvFrank Burk

Inbunden, Engelska, 1997

Del 32 i serien Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts

2 356 kr

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Beskrivning

A superb text on the fundamentals of Lebesgue measure and integration. This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for R and Lebesgue integration for extended real-valued functions on R. Starting with a thorough presentation of the preliminary concepts of undergraduate analysis, this book covers all the important topics, including measure theory, measurable functions, and integration. It offers an abundance of support materials, including helpful illustrations, examples, and problems. To further enhance the learning experience, the author provides a historical context that traces the struggle to define "area" and "area under a curve" that led eventually to Lebesgue measure and integration.Lebesgue Measure and Integration is the ideal text for an advanced undergraduate analysis course or for a first-year graduate course in mathematics, statistics, probability, and other applied areas. It will also serve well as a supplement to courses in advanced measure theory and integration and as an invaluable reference long after course work has been completed.

Produktinformation

Utgivningsdatum:1997-12-03
Mått:161 x 239 x 20 mm
Vikt:565 g
Format:Inbunden
Språk:Engelska
Serie:Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
Antal sidor:312
Förlag:John Wiley & Sons Inc
ISBN:9780471179788

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

FRANK BURK teaches in the Department of Mathematics at California State University.

Innehållsförteckning

Preface xiChapter 1. Historical Highlights 11.1 Rearrangements 21.2 Eudoxus (408-355 B.C.E.) and the Method of Exhaustion 31.3 The Lune of Hippocrates (430 B.C.E.) 51.4 Archimedes (287-212 B.C.E.) 71.5 Pierre Fermat (1601-1665)1.6 Gottfried Leibnitz (1646-1716), Issac Newton (1642-1723) 121.7 Augustin-Louis Cauchy (1789-1857) 151.8 Bernhard Riemann (1826-1866) 171.9 Emile Borel (1871 -1956), Camille Jordan (1838-1922), Giuseppe Peano (1858-1932) 201.10 Henri Lebesgue (1875-1941), William Young (1863-1942) 221.11 Historical Summary 251.12 Why Lebesgue 26Chapter 2. Preliminaries 322.1 Sets 322.2 Sequences of Sets 342.3 Functions 352.4 Real Numbers 422.5 Extended Real Numbers 492.6 Sequences of Real Numbers 512.7 Topological Concepts of R 622.8 Continuous Functions 662.9 Differentiable Functions 732.10 Sequences of Functions 75Chapter 3. Lebesgue Measure 873.1 Length of Intervals 903.2 Lebesgue Outer Measure 933.3 Lebesgue Measurable Sets 1003.4 BorelSets 1123.5 "Measuring" 1153.6 Structure of Lebesgue Measurable Sets 120Chapter 4. Lebesgue Measurable Functions 1264.1 Measurable Functions 1264.2 Sequences of Measurable Functions 1354.3 Approximating Measurable Functions 1374.4 Almost Uniform Convergence 141Chapter 5. Lebesgue Integration 1475.1 The Riemann Integral 1475.2 The Lebesgue Integral for Bounded Functions on Sets of Finite Measure 1735.3 The Lebesgue Integral for Nonnegative Measurable Functions 1945.4 The Lebesgue Integral and Lebesgue Integrability 2245.5 Convergence Theorems 237Appendix A. Cantor's Set 252Appendix B. A Lebesgue Nonmeasurable Set 266Appendix C. Lebesgue, Not Borel 273Appendix D. A Space-Filling Curve 276Appendix E. An Everywhere Continuous, Nowhere Differentiable,Function 279