A concise introduction to the theory of integration, second edition

✍ Scribed by Daniel W. Stroock

• Publisher: Birkhäuser
• Year: 1994
• Tongue: English
• Leaves: 191
• Edition: 2°
• Category: Library

✦ Synopsis

This edition develops the basic theory of Fourier transform. Stroock's approach is the one taken originally by Norbert Wiener and the Parseval's formula, as well as the Fourier inversion formula via Hermite functions. New exercises and solutions have been added for this edition.

✦ Table of Contents

Cover......Page 1
Title......Page 2
Copyright Page......Page 3
Contents......Page 4
Preface to the First Edition......Page 6
Preface to the Second Edition......Page 7
1.1: Riemann Integration......Page 8
1.2: Riemann-Stieltjes Integration......Page 14
2.0: The Idea......Page 26
2.1: Existence......Page 28
2.2: Euclidean Invariance......Page 37
3.1: Measure Spaces......Page 41
3.2: Construction of Integrals......Page 47
3.3: Convergence of Integrals......Page 57
3.4: Lebesgue's Differentiation Theorem......Page 69
4.1: Fubini's Theorem......Page 75
4.2: Steiner Symmetrization and the Isodiametric Inequality......Page 81
5.0: Introduction......Page 87
5.1: Lebesgue Integrals vs Riemann Integrals......Page 88
5.2: Polar Coordinates......Page 92
5.3: Jacobi's Transformation and Surface Measure......Page 96
5.4: The Divergence Theorem......Page 110
6.1: Jensen, Minkowski and Holder......Page 121
6.2: The Lebesgue Spaces......Page 126
6.3: Convolution and Approximate Identities......Page 138
7.1: An Existence Theorem......Page 146
7.2: Hilbert Space and the Radon-Nikodym Theorem......Page 158
Notation......Page 166
Index......Page 169
Solution to Selected Problems......Page 191