Problems And Proofs In Real Analysis: Theory Of Measure And Integration

by James J Yeh

Overview

This volume consists of the proofs of 391 problems in Real Analysis: Theory of Measure and Integration (3rd Edition).Most of the problems in Real Analysis are not mere applications of theorems proved in the book but rather extensions of the proven theorems or related theorems. Proving these problems tests the depth of understanding of the theorems in the main text.This volume will be especially helpful to those who read Real Analysis in self-study and have no easy access to an instructor or an advisor.

Product Details

ISBN-13:	9789814578509
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	03/21/2014
Pages:	500
Product dimensions:	5.90(w) x 8.90(h) x 1.10(d)

Table of Contents

Preface viii

§1 Measure on a σ-algebra of Sets 1

§2 Outer Measures 43

§3 Lebesgue Measure on R 46

§4 Measurable Functions 78

§5 Completion of Measure Space 104

§6 Convergence a.e. and Convergence in Measure 107

§7 Integration of Bounded Functions on Sets of Finite Measure 132

§8 Integration of Nonnegative Functions 160

§9 Integration of Measurable Functions 192

§10 Signed Measures 266

§11 Absolute Continuity of a Measure 277

§12 Monotone Functions and Functions of Bounded Variation 290

§13 Absolutely Continuous Functions 314

§16 The L^p Spaces 353

§17 Relation among the L^p Spaces 386

§18 Bounded Linear Functionals on the L^p Spaces 424

§22 Lebesgue-Stieltjes Measure Spaces 431

§23 Product Measure Spaces 443

§24 Lebesgue Measure Space on the Euclidean Space 466

§25 Differentiation on the Euclidean Space 473