# Measure Theory

• J. L. Doob
Book

Part of the Graduate Texts in Mathematics book series (GTM, volume 143)

1. Front Matter
Pages i-xii
2. J. L. Doob
Pages 1-5
3. J. L. Doob
Pages 7-10
4. J. L. Doob
Pages 11-16
5. J. L. Doob
Pages 17-36
6. J. L. Doob
Pages 37-52
7. J. L. Doob
Pages 53-72
8. J. L. Doob
Pages 73-101
9. J. L. Doob
Pages 103-121
10. J. L. Doob
Pages 123-143
11. J. L. Doob
Pages 145-156
12. J. L. Doob
Pages 157-177
13. J. L. Doob
Pages 179-204
14. Back Matter
Pages 205-212

### Introduction

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.

### Keywords

Conditional probability Distribution Hilbert space Maxima Probability distribution Probability space Probability theory Random variable Uniform integrability measure theory

• J. L. Doob
• 1
1. 1.UrbanaUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-0877-8
• Copyright Information Springer-Verlag New York, Inc. 1994
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-6931-1
• Online ISBN 978-1-4612-0877-8
• Series Print ISSN 0072-5285