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Measure and Category - A Survey of the Analogies between Topological and Measure Spaces (Hardcover, 2nd ed. 1980. 4th printing 1996)
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Measure and Category - A Survey of the Analogies between Topological and Measure Spaces (Hardcover, 2nd ed. 1980. 4th printing 1996)
Series: Graduate Texts in Mathematics, 2
Expected to ship within 10 - 17 working days
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In this edition, a set of Supplementary Notes and Remarks has been
added at the end, grouped according to chapter. Some of these call
attention to subsequent developments, others add further
explanation or additional remarks. Most of the remarks are
accompanied by a briefly indicated proof, which is sometimes
different from the one given in the reference cited. The list of
references has been expanded to include many recent contributions,
but it is still not intended to be exhaustive. John C. Oxtoby Bryn
Mawr, April 1980 Preface to the First Edition 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.
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