Applied nonstandard analysis
Author(s)
Bibliographic Information
Applied nonstandard analysis
（Pure and applied mathematics）（A Wiley-Interscience publication）
Wiley, c1977
Available at / 58 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc19:517/d2952020945054
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Note
Bibliography: p. 178
Includes index
Description and Table of Contents
Description
Geared toward upper-level undergraduates and graduate students, this text explores the applications of nonstandard analysis without assuming any 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 through a nonstandard treatment of the basic topics of elementary real analysis, topological spaces, and Hilbert space.
Important topics 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. Ever mindful of the needs of readers with little background in these subjects, the text offers a straightforward treatment that provides a strong foundation for advanced studies of analysis
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