Measure Theory: Second Edition

✍ Scribed by Donald L. Cohn (auth.)

• Publisher: Birkhäuser Basel
• Year: 2013
• Tongue: English
• Leaves: 466
• Series: Birkhäuser Advanced Texts Basler Lehrbücher
• Edition: 2
• Category: Library

✦ Synopsis

Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings.

Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.

✦ Table of Contents

Front Matter....Pages i-xxi
Measures....Pages 1-40
Functions and Integrals....Pages 41-77
Convergence....Pages 79-111
Signed and Complex Measures....Pages 113-141
Product Measures....Pages 143-154
Differentiation....Pages 155-179
Measures on Locally Compact Spaces....Pages 181-237
Polish Spaces and Analytic Sets....Pages 239-277
Haar Measure....Pages 279-306
Probability....Pages 307-371
Back Matter....Pages 373-457

✦ Subjects

Measure and Integration; Analysis; Probability Theory and Stochastic Processes