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. Republication of the 1937 edition.
Linear Integral Equations by William Vernon Lovitt Readable and systematic, this volume offers coherent presentations of not only the general theory of linear equations with a single integration, but also of applications to differential equations, the calculus of variations, and special areas in mathematical physics. Topics i...
Counterexamples in Analysis by Bernard R. Gelbaum, John M. H. Olmsted These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
Real Variables with Basic Metric Space Topology by Robert B. Ash Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition.
