Graduate Texts in Mathematics

Measure and Category

A Survey of the Analogies between Topological and Measure Spaces

Authors: Oxtoby, J. C.

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About this Textbook

This book has two main themes: the Baire category theorem as a method for proving existence, and the "duality" between measure and category. The category method is illustrated by a variety of typical applications, and the analogy between measure and category is explored in all of its ramifications. To this end, the elements of metric topology are reviewed and the principal properties of Lebesgue measure are derived. It turns out that Lebesgue integration is not essential for present purposes, the Riemann integral is sufficient. Concepts of general measure theory and topology are introduced, but not just for the sake of generality. Needless to say, the term "category" refers always to Baire category; it has nothing to do with the term as it is used in homological algebra. A knowledge of calculus is presupposed, and some familiarity with the algebra of sets. The questions discussed are ones that lend themselves naturally to set-theoretical formulation. The book is intended as an introduction to this kind of analysis. It could be used to supplement a standard course in real analysis, as the basis for a seminar, or for inde­ pendent study. It is primarily expository, but a few refinements of known results are included, notably Theorem 15.6 and Proposition 20A. The references are not intended to be complete. Frequently a secondary source is cited, where additional references may be found.

Table of contents (22 chapters)

Buy this book

eBook $14.99
price for USA in USD (gross)
  • ISBN 978-1-4615-9964-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Measure and Category
Book Subtitle
A Survey of the Analogies between Topological and Measure Spaces
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
2
Copyright
1971
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-1-4615-9964-7
DOI
10.1007/978-1-4615-9964-7
Series ISSN
0072-5285
Edition Number
1
Topics