Measure theory Donald L. Cohn

Format:

Book

Author/Creator:

Cohn, Donald L., 1942-

Series:

Birkhäuser advanced texts

Language:

English

Subjects (All):

Measure theory.

Physical Description:

1 online resource

Edition:

2nd ed.

Place of Publication:

New York, NY Birkhäuser ©2013

Summary:

Intended as a self-contained introduction to measure theory, this textbook also includesa 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 ofessential background material. The author aims to present a straightforward treatment of the part of measure theory necessary for analysis and probability' assuming only basic knowledge of analysis and topology ... Each chapter includes numerous well-chosen exercises, varying from very routine practice problems to important extensions and developments of the theory; for the difficult ones there are helpful hints. It is the reviewer's opinion that the author has succeeded in his aim. In spite of its lack of new results, the selection and presentation of materials makes this a useful book for an introduction to measure and integration theory.-Mathematical Reviews (Review of the First Edition) The book is a comprehensive and clearly written textbook on measure and integration ... The book contains appendices on set theory, algebra, calculus and topology in Euclidean spaces, topological and metric spaces, and the Bochner integral. Each section of the book contains a number of exercises.-zbMATH (Review of the First Edition)

Contents:

1. Measures

Algebras and sigma-algebras

Measures

Outer measures

Lebesgue measure

Completeness and regularity

Dynkin classes

2. Functions and Integrals

Measurable functions

Properties that hold almost everywhere

The integral

Limit theorems

The Riemann integral

Measurable functions again, complex-valued functions, and image measures

3. Convergence

Modes of Convergence

Normed spaces

Definition of Lp̂ and Lp̂

Properties of Lp̂ and L-p

Dual spaces

4. Signed and Complex Measures

Signed and complex measures

Absolute continuity

Singularity

Functions of bounded variation

The duals of the Lp̂ spaces

5. Product Measures

Constructions

Fubini's theorem

Applications

6. Differentiation

Change of variable in Rd̂

Differentiation of measures

Differentiation of functions

7. Measures on Locally Compact Spaces

Locally compact spaces

The Riesz representation theorem

Signed and complex measures; duality

Additional properties of regular measures

The æ*̂-measurable sets and the dual of L1̂

Products of locally compact spaces

8. Polish Spaces and Analytic Sets

Polish spaces

Analytic sets

The separation theorem and its consequences

The measurability of analytic sets

Cross sections

Standard, analytic, Lusin, and Souslin spaces

9. Haar Measure

Topological groups

The existence and uniqueness of Haar measure

The algebras L1̂ (G) and M (G)

Appendices

A. Notation and set theory

B. Algebra

C. Calculus and topology in Rd̂

D. Topological spaces and metric spaces

E. The Bochner integral

F Liftings

G The Banach-Tarski paradox

H The Henstock-Kurzweil and McShane integralsBibliography

Index of notation

Index

Notes:

Includes bibliographical references and indexes

Online resource; title from PDF title page (SpringerLink, viewed July 24, 2013)

Other Format:

Print version Measure theory

ISBN:

9781461469568

1461469562

1461469554

9781461469551

OCLC:

853605715

Access Restriction:

Restricted for use by site license