Applied Nonstandard Analysis

Geared toward upper-level undergraduates and graduate students, this text assumes no knowledge of mathematical logic; it develops the key techniques of nonstandard analysis at the outset from a single, powerful construction. Then, beginning with a nonstandard construction of the real number system, it leads students thorough the basic topics of elementary real analysis, topological spaces, and Hilbert space. Important subjects include nonstandard treatments of equicontinuity, nonmeasurable sets, and the existence of Haar measure. The focus on compact operators on a Hilbert space includes the Bernstein-Robinson theorem on invariant subspaces, which was first proved with nonstandard methods. 1977 ed.