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.Download
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