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Real Analysis: Theory of Measure and Integration
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General Information
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Type.................: Ebook
Part Size............: 30,123,828 bytes




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Post Information
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Posted by............: ~tqw~

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Release Notes
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This monograph evolved from a set of lecture notes for a course entitled Real
Analysis that I taught at the University of California, Irvine. The subject of
this course is the theory of measure and integration. Its prerequisite is
advanced calculus. All of the necessary background material can be found, for
example, in R. C. Buck\'s Advanced Calculus. The course is primarily for
beginning graduate students in mathematics but the audience usually includes
students from other disciplines too. The first five chapters of this book
contain enough material for a one-year course. The remaining two chapters take
an academic quarter to cover.

Table Of Contents
Preface to the First Edition xiii
Preface to the Second Edition xvii
Notations xix
Part 1 Measure Spaces 1
1 Measure on a a -algebra of Sets 3
2 Outer Measures 28
3 Lebesgue Measure on R 41
4 Measurable Functions 70
5 Completion of Measure Space 95
6 Convergence a.e. and Convergence in Measure 100
Part 2 The Lebesgue Integral 127
7 Integration of Bounded Functions on Sets of Finite Measure 127
8 Integration of Nonnegative Functions 152
9 Integration of Measurable Functions 169
10 Signed Measures 202
11 Absolute Continuity of a Measure 224
Part 3 Differentiation and Integration 245
12 Monotone Functions and Functions of Bounded Variation 245
13 Absolutely Continuous Functions 270
14 Convex Functions 308
Part 4 The Classical Banach Spaces 323
15 Normed Linear Spaces 323
16 The LP Spaces 376
17 Relation among the Lp Spaces 412
18 Bounded Linear Functionals on the Lp Spaces 429
19 Integration on Locally Compact Hausdorff Space 445
Part 5 Extension of Additive Set Functions to Measures 481
20 Extension of Additive Set Functions on an Algebra 481
21 Extension of Additive Set Functions on a Semialgebra 496
22 Lebesgue-Stieltjes Measure Spaces 505
23 Product Measure Spaces 527
Part 6 Measure and Integration on the Euclidean Space 597
24 Lebesgue Measure Space on the Euclidean Space 597
25 Differentiation on the Euclidean Space 620
26 Change of Variable of Integration on the Euclidean Space 649
Part 7 Hausdorff Measures on the Euclidean Space 675
27 Hausdorff Measures 675
28 Transformations of Hausdorff Measures 694
29 Hausdorff Measures of Integral and Fractional Dimensions 705
Bibliography 727
Index 729

Product Details

* ISBN: 9812566546
* ISBN-13: 9789812566546
* Format: Paperback, 738pp
* Publisher: World Scientific Publishing Company, Incorporated
* Pub. Date: October 2006
* Edition Description: 2ND
* Edition Number: 2

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