Imprint Princeton, N.

### Table of Contents

Physical description xix, p. Series Princeton lectures in analysis ; 3. Online Available online.

Full view. Science Library Li and Ma. S84 Unknown. More options. Find it at other libraries via WorldCat Limited preview. Bibliography Includes bibliographical references p.

## Introduction to Real Analysis

Contents Foreword vii Introduction xv 1 Fourier series: completion xvi Limits of continuous functions xvi 3 Length of curves xvii 4 Differentiation and integration xviii 5 The problem of measure xviii Chapter 1. Measure Theory 1 1 Preliminaries 1 The exterior measure 10 3 Measurable sets and the Lebesgue measure 16 4 Measurable functions 7 4.

Approximation by simple functions or step functions 30 4. The Lebesgue differentiation theorem Good kernels and approximations to the identity 3 Differentiability of functions 3.

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Absolutely continuous functions 3. Adjoints 5. The boundary value problem and Dirichlet's principle 43 5 Exercises 6 Problems Chapter 6: Abstract Measure and Integration Theory 1 Abstract measure spaces 1. Metric exterior measures 1. Integration formula for polar coordinates 3. Maximal ergodic theorem 5.

Positive operators 6. Self-similarity 3 Space-filling curves 3. Dyadic correspondence 3. Regularity of sets when d 3 4. Here the focus is on the development of measure and integration theory, differentiation and integration, Hilbert spaces, and Hausdorff measure and fractals. This book reflects the objective of the series as a whole: to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. Elias M.

Stein is Professor of Mathematics at Princeton University. Rami Shakarchi received his Ph. Foreword vii Introduction xv 1Fourier series: completion xvi Limits of continuous functions xvi 3Length of curves xvii 4Differentiation and integration xviii 5The problem of measure xviii Chapter 1. Measure Theory 1 1Preliminaries 1 The exterior measure 10 3Measurable sets and the Lebesgue measure 16 4Measurable functions 7 4.

## Real Analysis: Measure Theory, Integration, and Hilbert Spaces by Elias M. Stein

Approximation by simple functions or step functions 30 4. The Lebesgue differentiation theorem Good kernels and approximations to the identity 3Differentiability of functions 3. Absolutely continuous functions 3. Adjoints 5. The boundary value problem and Dirichlet's principle 43 5Exercises 6Problems Chapter 6: Abstract Measure and Integration Theory 1Abstract measure spaces 1.

Metric exterior measures 1.

Integration formula for polar coordinates 3. Maximal ergodic theorem 5.

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Positive operators 6. Self-similarity 3Space-filling curves 3. Dyadic correspondence 3.

Regularity of sets when d 3 4. Du kanske gillar. Inbunden Engelska, Spara som favorit.