Nonstandard analysis and its applications /

This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topol...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Cutland, Nigel
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge [England] ; New York : Cambridge University Press, 1988.
Colección:London Mathematical Society student texts ; 10.
Temas:
Nonstandard mathematical analysis > Congresses.
Analyse mathématique non standard > Congrès.
MATHEMATICS > Applied.
Nonstandard mathematical analysis
Nonstandard-Analysis
Analyse mathématique non standard.
Conference papers and proceedings
Acceso en línea:Texto completo

MARC

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245 0 0 |a Nonstandard analysis and its applications /  |c edited by Nigel Cutland. 
260 |a Cambridge [England] ;  |a New York :  |b Cambridge University Press,  |c 1988. 
300 |a 1 online resource (xiii, 346 pages) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
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490 1 |a London Mathematical Society student texts ;  |v 10 
500 |a Papers presented at a conference held at the University of Hull in 1986. 
504 |a Includes bibliographical references and index. 
588 0 |a Print version record. 
520 |a This textbook is an introduction to non-standard analysis and to its many applications. Non standard analysis (NSA) is a subject of great research interest both in its own right and as a tool for answering questions in subjects such as functional analysis, probability, mathematical physics and topology. The book arises from a conference held in July 1986 at the University of Hull which was designed to provide both an introduction to the subject through introductory lectures, and surveys of the state of research. The first part of the book is devoted to the introductory lectures and the second part consists of presentations of applications of NSA to dynamical systems, topology, automata and orderings on words, the non- linear Boltzmann equation and integration on non-standard hulls of vector lattices. One of the book's attractions is that a standard notation is used throughout so the underlying theory is easily applied in a number of different settings. Consequently this book will be ideal for graduate students and research mathematicians coming to the subject for the first time and it will provide an attractive and stimulating account of the subject. 
505 0 |a Cover; Series Page; Title; Copyright; CONTENTS; PREFACE; CONTRIBUTORS; AN INVITATION TO NONSTANDARD ANALYSIS; INTRODUCTION; I.A SET OF HYPERREALS; I.1 CONSTRUCTION OF *R; I.1.1 Example; I.1.2 Definition; I.1.3 Definition; I.1.4 Example; I.1.5 Definition; I.1.6 Proposition; I.1.7 Definition; I.1.8 Lemma; I.2 INTERNAL SETS AND FUNCTIONS; I.2.1 Definition; I. 2.2 Example; I.2.3 Proposition; I.2.4 Corollary; I.2.5 Theorem (x1-saturation); I.2.6 Corollary; I.2.7 Proposition; I.2.8 Definition; I.2.9 Proposition; I.2.10 Definition; I.2.11 Exaaple; I.2.12 Proposition; I.3 INFINITESIMAL CALCULUS 
505 8 |a I.3.1 PropositionI. 3.2 Proposition; I.3.3 Proposition; I.3.4 Corollary; I.3.5 Proposition; I.3.6 Corollary; I.3.7 Theorem; II. SUPERSTRUCTURES AND LOEB MEASURES; II. 1 SUPERSTRUCTURES; II. 1.1 Definition; II. 1.2 Definition; II. 1.3 LeMMA; II. 1.4 Proposition; II. 2 LOEB MEASURES; II. 2.1 Exaaple; II. 2.2 Definition; II .2.3 Lemma; II. 2.4 Lemma; II .2.5 Theorem; II. 2.6 Exaaple; II. 2.7 Example; II. 2.8 Lemma; II. 2.10 Theorem; II. 2.11 Theorem; II. 2.12 Corollary; II. 3 BROWNIAN MOTION; II. 3.1 Definition; II. 3.2 Lemma; II. 3.3 Lemma; II. 3.4 Lemma; II. 3.4 Lemma; II. 3.6 Theorem 
505 8 |a III. SATURATION AND TOPOLOGYIII. 1 BEYOND x1-SATURATION; III. 1.1 Definition; III. 1.2 Theorem; III. 1.3 TheoreM; III. 1.4 Lemma; III. 2 GENERAL TOPOLOGY; III. 2.1 Proposition; III. 2.2 Proposition; III. 2.3 Proposition; III. 2.4 Proposition; III. 2.5 Example; III. 2.6 Proposition; III. 2.7 Tychonov's Theorem; III. 2.8 Alaoglu's Theorea; III. 2.9 Ascoli's Theorea; III. 2.10 Example; III. 3 COMPLETIONS, COMPACTIFICATIONS. AND NONSTANDARD HULLS; III. 3.1 Proposition; III. 3.2 Corollary; III. 3.3 Proposition; III. 3.4 Example; III. 3.5 Example; III. 3.6 Proposition; III. 3.7 Corollary; III. 3.8 Example 
505 8 |a III. 3.9 PropositionIV. THE TRANSFER PRINCIPLE; IV. 1 THE LANGUAGES L(V(S) AND L*(V(S)); IV. 1.1 Definition; IV. I .2 Example; IV. 2 LOS' THEOREM AND THE TRANSFER PRINCIPLE; IV. 2.1 Definition; IV. 2.2. Lemma; IV. 2.3 Los' Theorem; IV. 2.4 Transfer Principle; IV. 2.5 Internal Definition Principle; IV. 3 AXIOMATIC NONSTANDARD ANALYSIS; APPENDIX. ULTRAFILTERS; A.1 Proposition; A.2 Lemma; A.3 Lemma; A.4 Theorem; NOTES; REFERENCES; INFINITESIMALS IN PROBABILITY THEORY; 1. THE HYPERFINITE TIME LINE; Definition; 1.2 Proposition; 1.3 Corollary; 1.4 Theorem (Anderson (1982)) 
505 8 |a 2. UNIVERSAL AND HOMOGENEOUS PROBABILITY SPACES2.1 Proposition; 2.2 Proposition; Definition; Definition; 2.3 Theorem (Keisler (1984)); 3. STOCHASTIC PROCESSES; 3.1 Lemma; 3.2 Proposition; 3.3 Proposition; 4. PRODUCTS OF LOEB SPACES; 4.1 ExampIe; 4.2 Fubini Theorem for Loeb Measures (Keisler(1984)); 4.3 Theorem (Keisler (1984)); 5. LIFTINGS OF STOCHASTIC PROCESSES; Definition; 5.1 Proposition; Definition; 5.2 Lemma; Definition; 5.3 Proposition; 5.4 Example; 5.5 Example; 5.6 Example; 6. ADAPTED PROBABILITY SPACES; 6.1 Proposition; Definition; Definition; 6.2 Theorem; 7. ADAPTED DISTRIBUTIONS 
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650 0 |a Nonstandard mathematical analysis  |v Congresses. 
650 0 |a Nonstandard mathematical analysis  |x Congresses. 
650 6 |a Analyse mathématique non standard  |x Congrès. 
650 6 |a Analyse mathématique non standard  |v Congrès. 
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650 7 |a Nonstandard mathematical analysis  |2 fast 
650 7 |a Nonstandard-Analysis  |2 gnd 
650 7 |a Analyse mathématique non standard.  |2 ram 
655 7 |a Conference papers and proceedings  |2 fast 
700 1 |a Cutland, Nigel. 
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