Verfügbarkeit: Infinitesimal analysis

Infinitesimal analysis:

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Bibliographische Detailangaben
1. Verfasser:	Gordon, Evgenij I. (VerfasserIn)
Format:	Buch
Sprache:	English Russian
Veröffentlicht:	Dordrecht Kluwer Academic Publishers 2002
Schriftenreihe:	Mathematics and its applications 544
Schlagworte:	Nonstandard mathematical analysis Infinitesimalanalysis
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Includes bibliographical references (p. [385]-413) and indexes
Beschreibung:	xiii, 422 p. ill. : 25 cm
ISBN:	1402007388

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MARC


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Datensatz im Suchindex

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adam_text	INFINITESIMAL ANALYSIS BY E.I. GORDON EASTERN ILLINOIS UNIVERSITY, CHARLESTON, ILLINOIS, U.S.A. A.G. KUSRAEV VLADIKAVKAZ STATE UNIVERSITY, VLADIKAVKAZ, RUSSIA AND S.S. KUTATELADZE SOBOLEV INSTITUTE OF MATHEMATICS, SIBERIAN DIVISION OF THE RUSSIAN ACADEMY OF SCIENCES, NOVOSIBIRSK, RUSSIA KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON CONTENTS FOREWORD IX CHAPTER 1. EXCURSUS INTO THE HISTORY OF CALCULUS 1 § 1.1. G. W. LEIBNIZ AND I. NEWTON 2 § 1.2. L. EULER 5 § 1.3. G. BERKELEY 5 § 1.4. J. D ALEMBERT AND L. CARNOT 6 § 1.5. B. BOLZANO, A. CAUCHY, AND K. WEIERSTRASS 7 § 1.6. N. N. LUZIN 7 § 1.7. A. ROBINSON 9 CHAPTER 2. NAIVE FOUNDATIONS OF INFINITESIMAL ANALYSIS 10 § 2.1. THE CONCEPT OF SET IN INFINITESIMAL ANALYSIS 10 § 2.2. PRELIMINARIES ON STANDARD AND NONSTANDARD REALS 16 § 2.3. BASICS OF CALCULUS ON THE REAL AXIS 23 CHAPTER 3. SET-THEORETIC FORMALISMS OF INFINITESIMAL ANALYSIS 35 § 3.1. THE LANGUAGE OF SET THEORY 37 § 3.2. ZERMELO-FRAENKEL SET THEORY 47 § 3.3. NELSON INTERNAL SET THEORY 64 5 3.4. EXTERNAL SET THEORIES .. . . 72 VI CONTENTS § 3.5. CREDENDA OF INFINITESIMAL ANALYSIS 80 § 3.6. VON NEUMANN-GODEL-BERNAYS THEORY 85 § 3.7. NONSTANDARD CLASS THEORY 94 § 3.8. CONSISTENCY OF NCT 101 § 3.9. RELATIVE INTERNAL SET THEORY 106 CHAPTER 4. MONADS IN GENERAL TOPOLOGY 116 § 4.1. MONADS AND FILTERS 116 § 4.2. MONADS AND TOPOLOGICAL SPACES 123 § 4.3. NEARSTANDARDNESS AND COMPACTNESS 126 § 4.4. INFINITE PROXIMITY IN UNIFORM SPACE 129 § 4.5. PRENEARSTANDARDNESS, COMPACTNESS, AND TOTAL BOUNDEDNESS .. 133 § 4.6. RELATIVE MONADS 140 § 4.7. COMPACTNESS AND SUBCONTINUITY 148 § 4.8. CYCLIC AND EXTENSIONAL FILTERS 151 § 4.9. ESSENTIAL AND PROIDEAL POINTS OF CYCLIC MONADS 156 § 4.10. DESCENDING COMPACT AND PRECOMPACT SPACES 159 § 4.11. PROULTRAFILTERS AND EXTENSIONAL FILTERS 160 CHAPTER 5. INFINITESIMALS AND SUB DIFFERENTIALS 166 § 5.1. VECTOR TOPOLOGY 166 § 5.2. CLASSICAL APPROXIMATING AND REGULARIZING CONES 170 § 5.3. KURATOWSKI AND ROCKAFELLAR LIMITS 180 § 5.4. APPROXIMATION GIVEN A SET OF INFINITESIMALS 189 § 5.5. APPROXIMATION TO COMPOSITES 199, § 5.6. INFINITESIMAL SUBDIFFERENTIALS 204 § 5.7. INFINITESIMAL OPTIMALITY 219 CONTENTS VII CHAPTER 6. TECHNIQUE OF HYPERAPPROXIMATION 223 § 6.1. NONSTANDARD HULLS 224 § 6.2. DISCRETE APPROXIMATION IN BANACH SPACE 233 § 6.3. LOEB MEASURE 242 § 6.4. HYPERAPPROXIMATION OF MEASURE SPACE 252 § 6.5. HYPERAPPROXIMATION OF INTEGRAL OPERATORS 262 § 6.6. PSEUDOINTEGRAL OPERATORS AND RANDOM LOEB MEASURES 272 CHAPTER 7. INFINITESIMALS IN HARMONIC ANALYSIS 281 § 7.1. HYPERAPPROXIMATION OF THE FOURIER TRANSFORM ON THE REALS ... 281 § 7.2. A NONSTANDARD HULL OF A HYPERFINITE GROUP 294 § 7.3. THE CASE OF A COMPACT NONSTANDARD HULL 307 § 7.4. HYPERAPPROXIMATION OF LOCALLY COMPACT ABELIAN GROUPS .... 316 § 7.5. EXAMPLES OF HYPERAPPROXIMATION 327 § 7.6. DISCRETE APPROXIMATION OF FUNCTION SPACES ON A LOCALLY COMPACT ABELIAN GROUP 340 § 7.7. HYPERAPPROXIMATION OF PSEUDODIFFERENTIAL OPERATORS 355 CHAPTER 8. EXERCISES AND UNSOLVED PROBLEMS 367 § 8.1. NONSTANDARD HULLS AND LOEB MEASURES 367 § 8.2. HYPERAPPROXIMATION AND SPECTRAL THEORY 369 § 8.3. COMBINING NONSTANDARD METHODS 371 § 8.4. CONVEX ANALYSIS AND EXTREMAL PROBLEMS 374 § 8.5. MISCELLANY 376 APPENDIX , 380 REFERENCES 385 NOTATION INDEX 414 SUBJECT INDEX 417
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spelling	Gordon, Evgenij I. Verfasser aut Infinitesimal analysis by E.I. Gordon, A.G. Kusraev, and S.S. Kutateladze Dordrecht Kluwer Academic Publishers 2002 xiii, 422 p. ill. : 25 cm txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 544 Includes bibliographical references (p. [385]-413) and indexes Nonstandard mathematical analysis Infinitesimalanalysis (DE-588)4161657-1 gnd rswk-swf Infinitesimalanalysis (DE-588)4161657-1 s DE-604 Kusraev, A. G. Sonstige oth Kutateladze, Semen S. 1945- Sonstige (DE-588)123299268 oth Mathematics and its applications 544 (DE-604)BV008163334 544 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940626&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Gordon, Evgenij I. Infinitesimal analysis Mathematics and its applications Nonstandard mathematical analysis Infinitesimalanalysis (DE-588)4161657-1 gnd
subject_GND	(DE-588)4161657-1
title	Infinitesimal analysis
title_auth	Infinitesimal analysis
title_exact_search	Infinitesimal analysis
title_full	Infinitesimal analysis by E.I. Gordon, A.G. Kusraev, and S.S. Kutateladze
title_fullStr	Infinitesimal analysis by E.I. Gordon, A.G. Kusraev, and S.S. Kutateladze
title_full_unstemmed	Infinitesimal analysis by E.I. Gordon, A.G. Kusraev, and S.S. Kutateladze
title_short	Infinitesimal analysis
title_sort	infinitesimal analysis
topic	Nonstandard mathematical analysis Infinitesimalanalysis (DE-588)4161657-1 gnd
topic_facet	Nonstandard mathematical analysis Infinitesimalanalysis
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009940626&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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