Boolean algebras in analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Academic Publ.
2002
|
| Schriftenreihe: | Mathematics and its applications
540 |
| Schlagworte: | |
| Online-Zugang: | Table of contents Inhaltsverzeichnis |
| Beschreibung: | XXI, 604 S. graph. Darst. |
| ISBN: | 140200480X |
Internformat
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Datensatz im Suchindex
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| adam_text | BOOLEAN ALGEBRAS IN ANALYSIS BY D.A. VLADIMIROV (F) FORMERLY OF ST.
PETERSBURG STATE UNIVERSITY, ST. PETERSBURG KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON CONTENTS FOREWORD TO THE ENGLISH TRANSLATION
IX DENIS ARTEM EVICH VLADIMIROV (1929-1994) XI PREFACE XVII INTRODUCTION
XIX PART I GENERAL THEORY OF BOOLEAN ALGEBRAS 0. PRELIMINARIES ON
BOOLEAN ALGEBRAS 3 1 LATTICES 3 2 BOOLEAN ALGEBRAS 10 3 ADDITIVE
FUNCTIONS ON BOOLEAN ALGEBRAS. MEASURES. RELATION TO PROBABILITY THEORY
23 4 AUTOMORPHISMS AND INVARIANT MEASURES 29 1. THE BASIC APPARATUS 35 1
SUBALGEBRAS AND GENERATORS 35 2 THE CONCEPTS OF IDEAL, FILTER, AND BAND
48 3 FACTORIZATION, HOMOMORPHISMS, INDEPENDENCE, AND FREE BOOLEAN
ALGEBRAS 55 2. COMPLETE BOOLEAN ALGEBRAS 83 1 COMPLETE BOOLEAN ALGEBRAS;
THEIR SUBALGEBRAS AND HOMOMORPHISMS 83 2 THE EXHAUSTION PRINCIPLE AND
THE THEOREM OF SOLID CORES 89 3 CONSTRUCTION OF COMPLETE BOOLEAN
ALGEBRAS 95 4 IMPORTANT EXAMPLES OF COMPLETE BOOLEAN ALGEBRAS 102 5 THE
BOOLEAN ALGEBRA OF REGULAR OPEN SETS 103 VI BOOLEAN ALGEBRAS IN ANALYSIS
6 THE TYPE, WEIGHT, AND CARDINALITY OF A COMPLETE BOOLEAN ALGEBRA 105 7
STRUCTURE OF A COMPLETE BOOLEAN ALGEBRA 111 3. REPRESENTATION OF BOOLEAN
ALGEBRAS 125 1 THE STONE THEOREM 125 2 INTERPRETATION OF THE BASIC
NOTIONS OF THE THEORY OF BOOLEAN ALGEBRAS IN THE LANGUAGE OF STONE
SPACES 136 3 STONE FUNCTORS 150 4. TOPOLOGIES ON BOOLEAN ALGEBRAS 181 1
DIRECTED SETS AND GENERALIZED SEQUENCES 181 2 VARIOUS TOPOLOGIES ON
BOOLEAN ALGEBRAS 184 3 REGULAR BOOLEAN ALGEBRAS. VARIOUS FORMS OF
DISTRIBUTIVITY 223 5. HOMOMORPHISMS 233 1 EXTENSION OF HOMOMORPHISMS 234
2 LIFTING 238 3 EXTENSION OF CONTINUOUS HOMOMORPHISMS 244 4 AGAIN ON
REPRESENTATION OF A BOOLEAN ALGEBRA 267 6. VECTOR LATTICES AND BOOLEAN
ALGEBRAS 277 1 K-SPACES AND THE RELATED BOOLEAN ALGEBRAS 277 2 SPECTRAL
FAMILIES AND RESOLUTIONS OF THE IDENTITY. SPECTRAL MEASURES 287 3
SEPARABLE BOOLEAN ALGEBRAS AND CR-ALGEBRAS OF SETS. MEASURABLE FUNCTIONS
296 4 THE INTEGRAL WITH RESPECT TO A SPECTRAL MEASURE AND THE
FREUDENTHAL THEOREM. THE SPACE && AS THE FAMILY OF RESOLUTIONS OF THE
IDENTITY. FUNCTIONS OF ELEMENTS 298 PART II METRIC THEORY OF BOOLEAN
ALGEBRAS 7. NORMED BOOLEAN ALGEBRAS 317 1 NORMED ALGEBRAS 317 2
EXTENSION OF A COUNTABLY ADDITIVE FUNCTION. THE LEBESGUE-CARATHEODORY
THEOREM 325 3 NBAS AND THE METRIC STRUCTURES OF MEASURE SPACES 332 4
TOTALLY ADDITIVE FUNCTIONS AND RESOLUTIONS OF THE IDENTITY OF A NORMED
ALGEBRA 342 5 SUBALGEBRAS OF A NORMED BOOLEAN ALGEBRA 353 6 FUNDAMENTAL
SYSTEMS OF PARTITIONS 382 7 SYSTEMS OF MEASURES AND THE LYAPUNOV THEOREM
387 CONTENTS VII 8. EXISTENCE OF A MEASURE 391 1 CONDITIONS FOR
EXISTENCE OF A MEASURE 391 2 EXISTENCE OF A MEASURE INVARIANT UNDER THE
AUTOMORPHISM GROUP 399 3 THE POTEPUN THEOREM 417 4 AUTOMORPHISMS OF
NORMABLE ALGEBRAS AND INVARIANT MEASURES 433 5 CONSTRUCTION OF A NORMED
BOOLEAN ALGEBRA GIVEN A TRANSFORMATION GROUP 439 9. STRUCTURE OF A
NORMED BOOLEAN ALGEBRA 445 1 STRUCTURE OF A NORMED ALGEBRA 445 2
CLASSIFICATION FOR NORMED ALGEBRAS 464 3 INTERLOCATION OF SUBALGEBRAS OF
A NORMED BOOLEAN ALGEBRA 470 4 ISOMORPHISM BETWEEN SUBALGEBRAS 475 5
ISOMORPHISM OF SYSTEMS OF SUBALGEBRAS 531 10. INDEPENDENCE 535 1 A
SYSTEM OF TWO SUBALGEBRAS 535 2 A TEST FOR METRIC INDEPENDENCE 541
APPENDICES 562 PREREQUISITES TO SET THEORY AND GENERAL TOPOLOGY 563 1
GENERAL REMARKS 563 2 PARTIALLY ORDERED SETS 564 3 TOPOLOGIES 565 BASICS
OF BOOLEAN VALUED ANALYSIS 569 1 GENERAL REMARKS 569 2 BOOLEAN VALUED
MODELS 569 3 PRINCIPLES OF BOOLEAN VALUED ANALYSIS 571 4 ASCENDING AND
DESCENDING 572 REFERENCES 581 INDEX 601
|
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| dewey-sort | 3511.3 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:00:11Z |
| institution | BVB |
| isbn | 140200480X |
| language | English Russian |
| lccn | 2002280831 |
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| physical | XXI, 604 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Kluwer Academic Publ. |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Vladimirov, Denis A. Verfasser aut Boolean algebras in analysis by D. A. Vladimirov Dordrecht [u.a.] Kluwer Academic Publ. 2002 XXI, 604 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 540 Algebra, Boolean Boolesche Algebra (DE-588)4146280-4 gnd rswk-swf Boolesche Algebra (DE-588)4146280-4 s DE-604 Mathematics and its applications 540 (DE-604)BV008163334 540 http://www.loc.gov/catdir/toc/fy031/2002280831.html Table of contents HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012892846&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vladimirov, Denis A. Boolean algebras in analysis Mathematics and its applications Algebra, Boolean Boolesche Algebra (DE-588)4146280-4 gnd |
| subject_GND | (DE-588)4146280-4 |
| title | Boolean algebras in analysis |
| title_auth | Boolean algebras in analysis |
| title_exact_search | Boolean algebras in analysis |
| title_full | Boolean algebras in analysis by D. A. Vladimirov |
| title_fullStr | Boolean algebras in analysis by D. A. Vladimirov |
| title_full_unstemmed | Boolean algebras in analysis by D. A. Vladimirov |
| title_short | Boolean algebras in analysis |
| title_sort | boolean algebras in analysis |
| topic | Algebra, Boolean Boolesche Algebra (DE-588)4146280-4 gnd |
| topic_facet | Algebra, Boolean Boolesche Algebra |
| url | http://www.loc.gov/catdir/toc/fy031/2002280831.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012892846&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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