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000733771 0247_ $$a10.1007/978-94-017-7327-0$$2doi
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000733771 049__ $$aISEA
000733771 050_4 $$aQA299.82
000733771 08204 $$a515$$223
000733771 24500 $$aNonstandard analysis for the working mathematician$$h[electronic resource] /$$cPeter A. Loeb and Manfred P.H. Wolff, editors.
000733771 250__ $$aSecond edition.
000733771 264_1 $$aDordrecht :$$bSpringer,$$c2015.
000733771 264_4 $$c©2015
000733771 300__ $$a1 online resource.
000733771 336__ $$atext$$btxt$$2rdacontent
000733771 337__ $$acomputer$$bc$$2rdamedia
000733771 338__ $$aonline resource$$bcr$$2rdacarrier
000733771 504__ $$aIncludes bibliographical references and index.
000733771 5050_ $$aSimple Nonstandard Analysis and Applications -- An Introduction to General Nonstandard Analysis -- Topology and Measure Theory -- Banach Spaces and Linear Operators -- General and End Compactifications -- Measure theory and integration -- Stochastic Analysis -- New Understanding of Stochastic Independence -- Nonstandard Analysis in Mathematical Economics -- Density Problems and Freiman's Inverse Problem -- Hypernatural numbers as ultrafilters.
000733771 506__ $$aAccess limited to authorized users.
000733771 520__ $$aStarting 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.
000733771 588__ $$aOnline resource; title from PDF title page (viewed August 31, 2015).
000733771 650_0 $$aNonstandard mathematical analysis.
000733771 7001_ $$aLoeb, Peter A.,$$eeditor.
000733771 7001_ $$aWolff, Manfred P.H.,$$eeditor.
000733771 77608 $$iPrint version:$$z9789401773263
000733771 852__ $$bebk
000733771 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-94-017-7327-0$$zOnline Access$$91397441.1
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