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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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [England] ; New York :
Cambridge University Press,
1988.
|
| Schriftenreihe: | London Mathematical Society student texts ;
10. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | Papers presented at a conference held at the University of Hull in 1986. |
| Beschreibung: | 1 online resource (xiii, 346 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781139172110 1139172115 9781107087934 1107087937 |
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| 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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| contents | 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 |
| ctrlnum | (OCoLC)818223030 |
| dewey-full | 519.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.4 |
| dewey-search | 519.4 |
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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</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="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))</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2. 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| genre | Conference papers and proceedings fast |
| genre_facet | Conference papers and proceedings |
| id | ZDB-4-EBA-ocn818223030 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:03Z |
| institution | BVB |
| isbn | 9781139172110 1139172115 9781107087934 1107087937 |
| language | English |
| oclc_num | 818223030 |
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| physical | 1 online resource (xiii, 346 pages) |
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| publishDate | 1988 |
| publishDateSearch | 1988 |
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| series | London Mathematical Society student texts ; |
| series2 | London Mathematical Society student texts ; |
| spelling | Nonstandard analysis and its applications / edited by Nigel Cutland. Cambridge [England] ; New York : Cambridge University Press, 1988. 1 online resource (xiii, 346 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society student texts ; 10 Papers presented at a conference held at the University of Hull in 1986. Includes bibliographical references and index. Print version record. 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. 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 Nonstandard mathematical analysis Congresses. Analyse mathématique non standard Congrès. MATHEMATICS Applied. bisacsh Nonstandard mathematical analysis fast Nonstandard-Analysis gnd http://d-nb.info/gnd/4137021-1 Analyse mathématique non standard. ram Conference papers and proceedings fast Cutland, Nigel. http://id.loc.gov/authorities/names/n79048335 has work: Nonstandard analysis and its applications (Text) https://id.oclc.org/worldcat/entity/E39PCFCBRcxyyqkb6cQHFGBmq3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Nonstandard analysis and its applications. Cambridge, [England] ; New York : Cambridge University Press, 1988 052135109X (DLC) 88016194 (OCoLC)18013779 London Mathematical Society student texts ; 10. http://id.loc.gov/authorities/names/n84727069 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=570393 Volltext |
| spellingShingle | Nonstandard analysis and its applications / London Mathematical Society student texts ; 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 Nonstandard mathematical analysis Congresses. Analyse mathématique non standard Congrès. MATHEMATICS Applied. bisacsh Nonstandard mathematical analysis fast Nonstandard-Analysis gnd http://d-nb.info/gnd/4137021-1 Analyse mathématique non standard. ram |
| subject_GND | http://d-nb.info/gnd/4137021-1 |
| title | Nonstandard analysis and its applications / |
| title_auth | Nonstandard analysis and its applications / |
| title_exact_search | Nonstandard analysis and its applications / |
| title_full | Nonstandard analysis and its applications / edited by Nigel Cutland. |
| title_fullStr | Nonstandard analysis and its applications / edited by Nigel Cutland. |
| title_full_unstemmed | Nonstandard analysis and its applications / edited by Nigel Cutland. |
| title_short | Nonstandard analysis and its applications / |
| title_sort | nonstandard analysis and its applications |
| topic | Nonstandard mathematical analysis Congresses. Analyse mathématique non standard Congrès. MATHEMATICS Applied. bisacsh Nonstandard mathematical analysis fast Nonstandard-Analysis gnd http://d-nb.info/gnd/4137021-1 Analyse mathématique non standard. ram |
| topic_facet | Nonstandard mathematical analysis Congresses. Analyse mathématique non standard Congrès. MATHEMATICS Applied. Nonstandard mathematical analysis Nonstandard-Analysis Analyse mathématique non standard. Conference papers and proceedings |
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