Covering all the standard topics, the author begins with a discussion of the integral in an abstract space, additive classes of sets, measurable functions, and integration of sequences of functions. Succeeding chapters cover Carathéodory measure; functions of bounded variation and the Lebesgue-Stieltjes integral; the derivation of additive functions of a set and of an interval; more.
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6 of 6 people found the following review helpful:
5.0 out of 5 stars
A classic and 5 stars for Dover!,
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This review is from: Theory of the Integral (Dover Books on Mathematics) (Hardcover)
I was looking for Saks' classical and beautiful treatment of integration for years but hesitated from buying it used (paperbacks usually look very ugly after 30 or 40 years). A great compliment has to go to Dover for reprinting it in their Phoenix series. Saks style of writing is clear and crisp in all respects. A special piece of sugar is the two articles of Banach in which he outlines a general point of view of integration.
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