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.