Theory of the integral,

S Saks

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.