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010   $a94-017-7327-0
024 7 $a10.1007/978-94-017-7327-0
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035   $a(EBL)4101887
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035   $a(PQKBManifestationID)16141207
035   $a(PQKBTitleCode)TC0001546578
035   $a(PQKBWorkID)14796574
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035   $a(DE-He213)978-94-017-7327-0
035   $a(MiAaPQ)EBC4101887
035   $a(PPN)188458026
035   $a(EXLCZ)993710000000467531
100   $a20150826d2015      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aNonstandard Analysis for the Working Mathematician /$fedited by Peter A. Loeb, Manfred P. H. Wolff
205   $a2nd ed. 2015.
210  1$aDordrecht :$cSpringer Netherlands :$cImprint: Springer,$d2015.
215   $a1 online resource (485 p.)
300   $aDescription based upon print version of record.
311   $a94-017-7326-2 
320   $aIncludes bibliographical references and index.
327   $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.
330   $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.
606   $aFunctional analysis
606   $aMeasure theory
606   $aOperator theory
606   $aGame theory
606   $aLogic, Symbolic and mathematical
606   $aNumber theory
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120
606   $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139
606   $aGame Theory, Economics, Social and Behav. Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13011
606   $aMathematical Logic and Foundations$3https://scigraph.springernature.com/ontologies/product-market-codes/M24005
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
615  0$aFunctional analysis.
615  0$aMeasure theory.
615  0$aOperator theory.
615  0$aGame theory.
615  0$aLogic, Symbolic and mathematical.
615  0$aNumber theory.
615 14$aFunctional Analysis.
615 24$aMeasure and Integration.
615 24$aOperator Theory.
615 24$aGame Theory, Economics, Social and Behav. Sciences.
615 24$aMathematical Logic and Foundations.
615 24$aNumber Theory.
676   $a510
702   $aLoeb$b Peter A$4edt$4http://id.loc.gov/vocabulary/relators/edt
702   $aWolff$b Manfred P. H$4edt$4http://id.loc.gov/vocabulary/relators/edt
906   $aBOOK
912   $a9910299767903321
996   $aNonstandard analysis for the working mathematician$91522911
997   $aUNINA