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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [England] ; New York :
Cambridge University Press,
1988.
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| Colección: | London Mathematical Society student texts ;
10. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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
- 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
- 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
- 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))
- 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