Nonstandard Analysis for the Working Mathematician

by Peter A. Loeb (Editor), Manfred P. H. Wolff (Editor)
Presents the version of nonstandard analysis that has had the greatest success and the widest scope of applications
Includes some of the most recent applications in various fields of mathematical analysis and probability
Each chapter, covering a different application of nonstandard analysis, begins with a gentle introduction for the non-expert

From the Back Cover
Starting with a simple formulation accessible to all mathematicians, this second edition is designed to provide a thorough introduction to nonstandard analysis. Nonstandard analysis is now a well-developed, powerful instrument for solving open problems in almost all disciplines of mathematics; it is often used as a ‘secret weapon’ by those who know the technique.

This book illuminates the subject with some of the most striking applications in analysis, topology, functional analysis, probability and stochastic analysis, as well as applications in economics and combinatorial number theory. The first chapter is designed to facilitate the beginner in learning this technique by starting with calculus and basic real analysis. The second chapter provides the reader with the most important tools of nonstandard analysis: the transfer principle, Keisler’s internal definition principle, the spill-over principle, and saturation. The remaining chapters of the book study different fields for applications; each begins with a gentle introduction before then exploring solutions to open problems.

All chapters within this second edition have been reworked and updated, with several completely new chapters on compactifications and number theory. Nonstandard Analysis for the Working Mathematician will be accessible to both experts and non-experts, and will ultimately provide many new and helpful insights into the enterprise of mathematics

Topics
Functional Analysis
Measure and Integration
Operator Theory
Game Theory, Economics, Social and Behav. Sciences
Mathematical Logic and Foundations
Number Theory