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 settheoretical 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)


Measure and Category on the Line
Pages 15

Liouville Numbers
Pages 69

Lebesgue Measure in rSpace
Pages 1018

The Property of Baire
Pages 1921

NonMeasurable Sets
Pages 2226

Table of contents (22 chapters)
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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

 J. C. Oxtoby
 Series Title
 Graduate Texts in Mathematics
 Series Volume
 2
 Copyright
 1971
 Publisher
 SpringerVerlag New York
 Copyright Holder
 SpringerVerlag New York
 eBook ISBN
 9781461599647
 DOI
 10.1007/9781461599647
 Series ISSN
 00725285
 Edition Number
 1