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Bibliographic Details
Main Author:	Schwartz, Laurent 1915-2002 (Author)
Format:	Book
Language:	English
Published:	London, [u.a.] Oxford University Press 1973
Series:	Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research studies in mathematics 6
Subjects:	Rotationssymmetrisches Werkstück Radon-Maß
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001764096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	xii, 393 Seiten Illustrationen

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MARC


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Record in the Search Index

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adam_text	CONTENTS Introduction . v * Remeeciements . vii PART I Summary of Chapter I . 3 Chapter I. Radon Measures: Main Properties and Operations 1. Preliminaries . 7 2. Definition of Radon measure on general topological spaces . 12 3. Induced measures . 20 4. Product of a measure by a locally integrable function 23 5. Measurable mappings and image measures . . 25 6. Other properties of Radon measures . 40 7. Real and complex measures . . . .53 8. Different ways of defining Radon measures . . 58 9. Tensor product of measures . 63 10. Projective limit of measures . 74 11. Non Hausdorff spaces . 82 Summary of Chapter II . . . . . .89 Chapter II. Polish, Lusin, Suslin and Radon Spaces 1. Definitions and topological properties . 92 2. Examples of Lusin spaces . . . .112 3. Radon spaces . . . . . .117 4. Lifting of Ln to J2?" 130 5. Spaces of regulated functions . . . .136 Terminological Index to Part I . . . . • 144 x contents References . . . . . . . . .146 PART II Introduction to Part II . . . . . .151 Summary of Chapter I . . . . . . .152 Chapter I. Equivalent Topologies 1. Equivalent measures . . . . .153 2. Equivalent topologies . . . . .155 3. A Borel graph theorem . . . . .160 4. Equivalence of the strong and weak topologies . 161 5. Equivalence of the strong topology with coarser topologies . . . . . . .166 Summary of Chapter II . . . . . . .171 Chapter II. Cylindrical Measures 1. Definition of cylindrical measures . . .172 2. Operations with cylindrical measures . . .180 3. Concentrations . . . . . . .188 Summary of Chapter III 206 Chapter III. Cylindrical Measures and Hilbert Sohmidt Operators 1. Hilbert Schmidt operators . 207 2. The main lemma 212 3. The theorem of Sazonov . . . . .214 Summary of Chapter IV . . . . . .218 CONTENTS Xi Chapter IV. Cylindrical Measures and Nuclear Spaces 1. Nuclear operators . . . . . .219 2. Nuclear spaces . 226 3. The theorem of Minlos 233 4. The theorem of Sazonov Badrikian . . . 237 Summary of Chapter V . 242 Chapter V. Cylindrical Measures and Probability theory 1. Basic concepts of probability theory . . . 244 2. Randon functions . 254 3. Examples and applications . 269 4. An analogue of Prokhorov's theorem for random variables with values in a Suslin space . . . 288 5. Categories of random functions . 305 Summary of Chapter VI . 324 Chapter VI. Gauss Measures 1. The definition of Gauss measures . . . 325 2. The Hilbert subspaces of a locally convex space . 330 3. The converse of the theorems of Sazonov and Minlos 341 4. The analogue of Sazonov's theorem for lp spaces (0 p + oo) and applications . . . 347 5. An application to Brownian motion . . .350 Summary of Appendix . 368 Appendix. Complements on Narrow Convergence 1. Narrow convergence on an arbitrary topological space . 369 2. Riemann integrable functions . 374 t Xii CONTENTS 3. A compactness criterion for the narrow topology . 379 4. A theorem of Paul LeVy 382 5. The space of finite measures on a Suslin space . 385 Terminological Index to Part II . . . . . 390 References . 392
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language	English
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physical	xii, 393 Seiten Illustrationen
publishDate	1973
publishDateSearch	1973
publishDateSort	1973
publisher	Oxford University Press
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series	Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research studies in mathematics
series2	Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research studies in mathematics
spellingShingle	Schwartz, Laurent 1915-2002 Radon measures on arbitrary topological spaces and cylindrical measures Tata Institute of Fundamental Research <Bombay>: Tata Institute of Fundamental Research studies in mathematics Rotationssymmetrisches Werkstück (DE-588)4178510-1 gnd Radon-Maß (DE-588)4242168-8 gnd
subject_GND	(DE-588)4178510-1 (DE-588)4242168-8
title	Radon measures on arbitrary topological spaces and cylindrical measures
title_auth	Radon measures on arbitrary topological spaces and cylindrical measures
title_exact_search	Radon measures on arbitrary topological spaces and cylindrical measures
title_full	Radon measures on arbitrary topological spaces and cylindrical measures Laurent Schwartz
title_fullStr	Radon measures on arbitrary topological spaces and cylindrical measures Laurent Schwartz
title_full_unstemmed	Radon measures on arbitrary topological spaces and cylindrical measures Laurent Schwartz
title_short	Radon measures on arbitrary topological spaces and cylindrical measures
title_sort	radon measures on arbitrary topological spaces and cylindrical measures
topic	Rotationssymmetrisches Werkstück (DE-588)4178510-1 gnd Radon-Maß (DE-588)4242168-8 gnd
topic_facet	Rotationssymmetrisches Werkstück Radon-Maß
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001764096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV004244858
work_keys_str_mv	AT schwartzlaurent radonmeasuresonarbitrarytopologicalspacesandcylindricalmeasures

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