LEADER 05608nam0 2200805 i 450 001 VAN00114033 005 20260702082025.162 017 70$2N$a9789401773270 035 40$a1591458128 100 $a20180124d2015 |0itac50 ba 101 $aeng 102 $aNL 105 $a|||| ||||| 181 $ai$b e 182 $ab 183 $acr 200 1 $aNonstandard analysis for the working mathematician$fPeter A. Loeb, Manfred P. H. Wolff editors 205 $a2. ed 210 $aDordrecht$cSpringer$d2015 215 $aXV, 481 p.$d24 cm 327 $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 500 1$3VAN00235168$aNonstandard Analysis for the Working Mathematician$91522911 606 $a03H05$xNonstandard models in mathematics [MSC 2020]$3VANC020826$2MF 606 $a03H10$xOther applications of nonstandard models (economics, physics, etc.) [MSC 2020]$3VANC033808$2MF 606 $a03H15$xNonstandard models of arithmetic [MSC 2020]$3VANC024402$2MF 606 $a11B05$xDensity, gaps, topology [MSC 2020]$3VANC031506$2MF 606 $a11B13$xAdditive bases, including sumsets [MSC 2020]$3VANC021817$2MF 606 $a11B30$xArithmetic combinatorics; higher degree uniformity [MSC 2020]$3VANC033810$2MF 606 $a11B75$xOther combinatorial number theory [MSC 2020]$3VANC022174$2MF 606 $a11U10$xNonstandard arithmetic (number-theoretic aspects) [MSC 2020]$3VANC024440$2MF 606 $a12L15$xNonstandard arithmetic and field theory [MSC 2020]$3VANC033809$2MF 606 $a26E35$xNonstandard analysis [MSC 2020]$3VANC021236$2MF 606 $a28E05$xNonstandard measure theory [MSC 2020]$3VANC021242$2MF 606 $a46B08$xUltraproduct techniques in Banach space theory [MSC 2020]$3VANC029573$2MF 606 $a46B20$xGeometry and structure of normed linear spaces [MSC 2020]$3VANC019996$2MF 606 $a46S20$xNonstandard functional analysis [MSC 2020]$3VANC020828$2MF 606 $a47A10$xSpectrum, resolvent [MSC 2020]$3VANC021619$2MF 606 $a47A58$xLinear operator approximation theory [MSC 2020]$3VANC020791$2MF 606 $a47D06$xOne-parameter semigroups and linear evolution equations [MSC 2020]$3VANC020305$2MF 606 $a47H09$xContraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc. [MSC 2020]$3VANC029083$2MF 606 $a47H10$xFixed-point theorems [MSC 2020]$3VANC020267$2MF 606 $a47S20$xNonstandard operator theory [MSC 2020]$3VANC021244$2MF 606 $a54D30$xCompactness [MSC 2020]$3VANC028929$2MF 606 $a54Jxx$xNonstandard topology [MSC 2020]$3VANC021241$2MF 606 $a60G51$xProcesses with independent increments; Lévy processes [MSC 2020]$3VANC020665$2MF 606 $a60H07$xStochastic calculus of variations and the Malliavin calculus [MSC 2020]$3VANC020014$2MF 606 $a60J65$xBrownian motion [MSC 2020]$3VANC020038$2MF 606 $a91Axx$xGame theory [MSC 2020]$3VANC020464$2MF 606 $a91Bxx$xMathematical economics [MSC 2020]$3VANC024654$2MF 610 $aBanach spaces$9KW:K 610 $aCombinatorial Number Theory$9KW:K 610 $aCompactifications$9KW:K 610 $aLinear operators$9KW:K 610 $aLoeb Probability Theory$9KW:K 610 $aMathematical Economics$9KW:K 610 $aNonstandard analysis$9KW:K 610 $aStochastic Analysis$9KW:K 620 $aNL$dDordrecht$3VANL000068 702 1$aLoeb$bPeter A.$3VANV088127 702 1$aWolff$bManfred P. H.$3VANV088128 712 $aSpringer $3VANV108073$4650 790 1$aWolff, E <1896-1954>$zWolff, Manfred P. H.$3VANV233156 801 $aIT$bSOL$c20260911$gRICA 856 4 $uhttp://dx.doi.org/10.1007/978-94-017-7327-0$zE-book ? Accesso al full-text attraverso riconoscimento IP di Ateneo, proxy e/o Shibboleth 899 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$1IT-CE0120$2VAN08 912 $fN 912 $aVAN00114033 950 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08DLOAD e-book 0351 $e08eMF351 20180124 996 $aNonstandard analysis for the working mathematician$91522911 997 $aUNICAMPANIA