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<図書>
Boolean algebras in analysis

責任表示 by D.A. Vladimirov
シリーズ Mathematics and its applications ; v. 540
データ種別 図書
出版者 Dordrecht : Kluwer Academic
出版年 c2002
本文言語 英語
大きさ xxi, 604 p. ; 25 cm
目次 Machine generated contents note: 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
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 a-algebras of sets.
Measurable functions 296
4 The integral with respect to a spectral measure and
the Freudenthal Theorem. The space 6y 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-Carath6odory 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
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.
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所蔵情報


理系図3F 数理独自 023212002001507 VLAD/10/2 2002

書誌詳細

著者標目 *Vladimirov, D. A. (Denis Artemʹevich)
書誌ID 1001400780
ISBN 140200480X
NCID BA56875773
巻冊次 ISBN:140200480X
登録日 2009.11.02
更新日 2009.11.02