Integral, measure, and ordering:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer [u.a.]
1997
|
| Schriftenreihe: | Mathematics and its applications
411 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 378 S. |
| ISBN: | 0792345665 8088683181 |
Internformat
MARC
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| 245 | 1 | 0 | |a Integral, measure, and ordering |c by Beloslav Riečan and Tibor Neubrunn |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer [u.a.] |c 1997 | |
| 300 | |a XIII, 378 S. | ||
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| 490 | 1 | |a Mathematics and its applications |v 411 | |
| 650 | 7 | |a Mesure, Théorie de la |2 ram | |
| 650 | 4 | |a Fuzzy sets | |
| 650 | 4 | |a Integrals, Generalized | |
| 650 | 4 | |a Measure theory | |
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Datensatz im Suchindex
| _version_ | 1804126484780023808 |
|---|---|
| adam_text | Contents
1 Sets and fuzzy sets 1
1.1 Sets and families of sets 1
1.2 Fuzzy sets and operations with them 7
1.3 Selected results from probability theory 9
2 Null sets and small systems 15
2.1 T ideals of null sets 15
2.2 Null sets and decompositions 17
2.3 Systems of small sets 20
2.4 Small systems and convergence 24
2.5 Small systems and fuzzy sets 25
Problems 30
Notes and comments 32
3 Measures on ordered spaces 34
3.1 Integrals on lattices 34
3.2 Range 41
3.3 Extension of integrals 46
3.4 Measure and integral 52
Problems 56
Notes and comments 57
4 Subadditive measures 59
4.1 Daniell integration scheme 59
4.2 Subadditive measure and integral 65
Problems 67
Notes and comments 68
5 The Kurzweil integral in ordered spaces 70
5.1 The idea of the Henstock Kurzweil integral 70
5.2 Definition and elementary properties 74
5.3 Henstock lemma and some of its consequences 82
5.4 Limit theorems 85
5.5 Operator valued measures 89
CONTENTS
5.6 Kurzweil Stieltjes integral 91
5.7 Moment problem 94
Problems 99
Notes and comments 101
6 Quantum logics 103
6.1 Motivation for studying measures on logics 103
6.2 Definition and examples of logics 105
6.3 Compatibility on logics 107
6.4 Boolean algebras embedded in a logic 110
6.5 Measurability on logics 114
6.6 Representation of observables on r logics 116
6.7 Joint observables 117
Problems 121
Notes and comments 124
7 Fuzzy quantum spaces 127
7.1 Basic notions 127
7.2 A representation lemma 129
7.3 Majorizing cr algebra 132
7.4 Joint observable 136
Problems 140
Notes and comments 141
8 Fuzzy quantum logics 142
8.1 States on a space of fuzzy sets 142
8.2 Observables 153
8.3 Joint observable 159
8.4 Kolmogorov construction 161
8.5 Almost everywhere convergence 166
8.6 Upper and lower limits 169
8.7 Individual ergodic theorem 178
Problems 180
Notes and comments 182
9 Probability on MV algebras 183
9.1 States and observables 183
9.2 Central limit theorem 187
9.3 Strong law of large numbers 191
9.4 Weakly ^ distributive MV algebras 193
9.5 Alexandrov s theorem 195
9.6 Construction of observables 199
9.7 Sum of observables 201
9.8 Upper and lower limit 206
Problems 211
Notes and comments 212
10 The entropy of fuzzy dynamical systems 213
10.1 Kolmogorov Sinai entropy 213
CONTENTS xiii
10.2 Algebraic entropy 218
10.3 Entropy in F quaiitum logics 227
10.4 Fuzzy generators 2.45
10.5 Entropy in / quantum spaces 230
10.6 g entropy 2 11
Problems 249
Notes and comments 250
11 Measurability and integrability of multifunctions 252
11.1 HaiisdorfF metric 252
11.2 Measurability of multifunctions 251
11.3 Measurable multifunction as a measurable function 255
11.4 Convergence of multifunctions on measure spaces 258
11.5 Further properties of measurable multifunctions 259
1 l.G Theorem on measurable selector 261
11.7 Integrable multifunction 263
11.8 Limit theorems for integrable multifunctions 265
11.9 Random sets 267
11.10 Fuzzy random variable 270
Problems 273
Notes and comments 276
Appendix A D posets (Ferdinand Chovanec, Frantisek Kopka) 278
A.I Difference posets 278
A.2 Difference lattices 285
A.3 Compatibility in D posets 291
A.4 States and observables on D posots 298
A.5 Ideals in D posets 307
Notes and comments 311
Appendix B Notes on order convergence and order topology
(Hana Kirchheimova, Zdenka Riecanova) 312
B.I Order convergence of nets and filters in partially ordered sets and
their MacNeille completions 312
B.2 Order topology and order topological lattices in language of filters
and nets 316
B.3 Metric modular ortholattices 320
Problems 324
Notes and comments 325
References 326
Index 374
|
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| id | DE-604.BV011898179 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:18:12Z |
| institution | BVB |
| isbn | 0792345665 8088683181 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008039809 |
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| physical | XIII, 378 S. |
| publishDate | 1997 |
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| publisher | Kluwer [u.a.] |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Riečan, Beloslav Verfasser aut Integral, measure, and ordering by Beloslav Riečan and Tibor Neubrunn Dordrecht [u.a.] Kluwer [u.a.] 1997 XIII, 378 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 411 Mesure, Théorie de la ram Fuzzy sets Integrals, Generalized Measure theory Neubrunn, Tibor Sonstige oth Mathematics and its applications 411 (DE-604)BV008163334 411 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008039809&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Riečan, Beloslav Integral, measure, and ordering Mathematics and its applications Mesure, Théorie de la ram Fuzzy sets Integrals, Generalized Measure theory |
| title | Integral, measure, and ordering |
| title_auth | Integral, measure, and ordering |
| title_exact_search | Integral, measure, and ordering |
| title_full | Integral, measure, and ordering by Beloslav Riečan and Tibor Neubrunn |
| title_fullStr | Integral, measure, and ordering by Beloslav Riečan and Tibor Neubrunn |
| title_full_unstemmed | Integral, measure, and ordering by Beloslav Riečan and Tibor Neubrunn |
| title_short | Integral, measure, and ordering |
| title_sort | integral measure and ordering |
| topic | Mesure, Théorie de la ram Fuzzy sets Integrals, Generalized Measure theory |
| topic_facet | Mesure, Théorie de la Fuzzy sets Integrals, Generalized Measure theory |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008039809&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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