Measure Theory Vol.2

Description

Measure theory is a classical area of mathematics born more than two thousand years ago. Nowadays it continues intensive development and has fruitful connections with most other fields of mathematics as well as important applications in physics.This book gives an exposition of the foundations of modern measure theory and offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course (the material of this level corresponds to a variety of special courses), and, finally, more specialized topics partly covered by more than 850 exercises.Volume 1 (Chapters 1-5) is devoted to the classical theory of measure and integral. Whereas the first volume presents the ideas that go back mainly to Lebesgue, the second volume (Chapters 6-10) is to a large extent the result of the later development up to the recent years. The central subjects in Volume 2 are: transformations of measures, conditional measures, and weak convergence of measures. These three topics are closely interwoven and form the heart of modern measure theory.The organization of the book does not require systematic reading from beginning to end; in particular, almost all sections in the supplements are independent of each other and are directly linked only to specific sections of the main part.The target readership includes graduate students interested in deeper knowledge of measure theory, instructors of courses in measure and integration theory, and researchers in all fields of mathematics. The book may serve as a source for many advanced courses or as a reference. Preface......Page 4 Table of Contents......Page 6 6. Borel, Baire and Souslin sets......Page 12 7. Measures on topological spaces......Page 78 8. Weak convergence of measures......Page 186 9. Transformations of measures and isomorphisms......Page 278 10. Conditional measures and conditional expectations......Page 350 Contents of Volume 1......Page 9 Subject Index......Page 572 Author Index......Page 558 Bibliographical and Historical Comments......Page 450 References......Page 476