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Real and Complex Analysis (International Edition)

Real and Complex Analysis (International Edition) - 3rd edition

ISBN13: 978-0071002769

Cover of Real and Complex Analysis (International Edition) 3RD 86 (ISBN 978-0071002769)
ISBN13: 978-0071002769
ISBN10: 0071002766
Cover type:
Edition/Copyright: 3RD 86
Publisher: McGraw-Hill Publishing Company
Published: 1986
International: Yes

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Real and Complex Analysis (International Edition) - 3RD 86 edition

ISBN13: 978-0071002769

Walter Rudin

ISBN13: 978-0071002769
ISBN10: 0071002766
Cover type:
Edition/Copyright: 3RD 86
Publisher: McGraw-Hill Publishing Company

Published: 1986
International: Yes
Summary

This is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject.

Table of Contents

Chapter 1. Abstract Integration

Set-theoretic notations and terminology
The concept of measurability
Simple functions
Elementary properties of measures
Arithmetic in [0, infinity]
Integration of positive functions
Integration of complex functions
The role played by sets of measure zero
Exercises

Chapter 2. Positive Borel Measures

Vector spaces
Topological preliminaries
The Riesz representation theorem
Regularity properties of Borel measures
Lebesgue measure
Continuity properties of measurable functions
Exercises

Chapter 3. L^p-Spaces

Convex functions and inequalities
The L^p-spaces
Approximation by continuous functions
Exercises

Chapter 4. Elementary Hilbert Space Theory

Inner products and linear functionals
Orthonormal sets
Trigonometric series
Exercises

Chapter 5. Examples of Banach Space Techniques

Banach spaces
Consequences of Baire's theorem
Fourier series of continuous functions
Fourier coefficients of L¹-functions

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