Graduate Texts in Mathematics - 143: Measure Theory

Joseph L. Doob

ISBN 10: 0387940553 / ISBN 13: 9780387940557

Published by Springer-Verlag, 1993

About this Item

Leichte Kratzer / Abnutzungen / Druckstellen; Farbtonänderung. This text is unique in accepting probability theory as an essential part of measure theory. Therefore, many examples are taken from probability, and probabilistic concepts such as independence and Markov processes are integrated into the text. Also, more attention than usual is paid to the role of algebras, and the metric defining the distance between sets as the measure of their symmetric difference is exploited more than is customary.

Seller Inventory # 083a0b2c-b0ba-4836-83c7-b94d151997a3

Bibliographic Details

• Title: Graduate Texts in Mathematics - 143: Measure Theory
• Publisher: Springer-Verlag
• Publication Date: 1993
• Language: English
• ISBN 10: 0387940553
• ISBN 13: 9780387940557
• Binding: Hardcover
• Condition: Fine
• Seller catalogs:
  • Mathematics

About this title

Synopsis

This book was planned originally not as a work to be published, but as an excuse to buy a computer, incidentally to give me a chance to organize my own ideas ~n what measure theory every would-be analyst should learn, and to detail my approach to the subject. When it turned out that Springer-Verlag thought that the point of view in the book had general interest and offered to publish it, I was forced to try to write more clearly and search for errors. The search was productive. Readers will observe the stress on the following points. The application of pseudometric spaces. Pseudo metric, rather than metric spaces, are applied to obviate the artificial replacement of functions by equivalence classes, a replacement that makes the use of "almost everywhere" either improper or artificial. The words "function" and "the set on which a function has values at least E" can be taken literally in this book. Pseudometric space properties are applied in many contexts. For example, outer measures are used to pseudometrize classes of sets and the extension of a finite measure from an algebra to a 0" algebra is thereby reduced to finding the closure of a subset of a pseudo metric space.