Boolean algebras in analysis
By: by D.A. Vladimirov.
Series: Mathematics and its applications ;; v. 540; Mathematics and its applications (Kluwer Academic Publishers) ;; v. 540.
Publisher: Kluwer Academic
Published: 2002
Place of publication: Dordrecht; Boston
Language: eng
Number of pages: 604
Subjects: Algebra, Boolean
Notes: Includes bibliographical references (p. 581-599) and index.
Table of contents: title: Machine generated contents note: Part I GENERAL THEORY OF BOOLEAN ALGEBRAS; title: 0. PRELIMINARIES ON BOOLEAN ALGEBRAS 3; title: 1 Lattices 3; title: 2 Boolean algebras 10; title: 3 Additive functions on Boolean algebras. Measures.; title: Relation to probability theory 23; title: 4 Automorphisms and invariant measures 29; title: 1. THE BASIC APPARATUS 35; title: 1 Subalgebras and generators 35; title: 2 The concepts of ideal, filter, and band 48; title: 3 Factorization, homomorphisms, independence, and; title: free Boolean algebras 55; title: 2. COMPLETE BOOLEAN ALGEBRAS 83; title: 1 Complete Boolean algebras; their subalgebras and; title: homomorphisms 83; title: 2 The exhaustion principle and the theorem of solid cores 89; title: 3 Construction of complete Boolean algebras 95; title: 4 Important examples of complete Boolean; title: algebras 102; title: 5 The Boolean algebra of regular open sets 103; title: 6 The type, weight, and cardinality of a complete Boolean; title: algebra 105; title: 7 Structure of a complete Boolean algebra 111; title: 3. REPRESENTATION OF BOOLEAN ALGEBRAS 125; title: 1 The Stone Theorem 125; title: 2 Interpretation of the basic notions of the theory of; title: Boolean algebras in the language of Stone spaces 136; title: 3 Stone functors 150; title: 4. TOPOLOGIES ON BOOLEAN ALGEBRAS 181; title: 1 Directed sets and generalized sequences 181; title: 2 Various topologies on Boolean algebras 184; title: 3 Regular Boolean algebras. Various forms of distributivity 223; title: 5. HOMOMORPHISMS 233; title: 1 Extension of homomorphisms 234; title: 2 Lifting 238; title: 3 Extension of continuous homomorphisms 244; title: 4 Again on representation of a Boolean algebra 267; title: 6. VECTOR LATTICES AND BOOLEAN ALGEBRAS 277; title: 1 K-spaces and the related Boolean algebras 277; title: 2 Spectral families and resolutions of the identity.; title: Spectral measures 287; title: 3 Separable Boolean algebras and a-algebras of sets.; title: Measurable functions 296; title: 4 The integral with respect to a spectral measure and; title: the Freudenthal Theorem. The space 6y as the family; title: of resolutions of the identity. Functions of elements 298; title: Part II METRIC THEORY OF BOOLEAN ALGEBRAS; title: 7. NORMED BOOLEAN ALGEBRAS 317; title: 1 Normed algebras 317; title: 2 Extension of a countably additive function.; title: The Lebesgue-Carath6odory Theorem 325; title: 3 NBAs and the metric structures of measure spaces 332; title: 4 Totally additive functions and resolutions of the identity; title: of a normed algebra 342; title: 5 Subalgebras of a normed Boolean algebra 353; title: 6 Fundamental systems of partitions 382; title: 7 Systems of measures and the Lyapunov Theorem 387; title: 8. EXISTENCE OF A MEASURE 391; title: 1 Conditions for existence of a measure 391; title: 2 Existence of a measure invariant under; title: the automorphism group 399; title: 3 The Potepun Theorem 417; title: 4 Automorphisms of normable algebras and; title: invariant measures 433; title: 5 Construction of a normed Boolean algebra given; title: a transformation group 439; title: 9. STRUCTURE OF A NORMED BOOLEAN ALGEBRA 445; title: 1 Structure of a normed algebra 445; title: 2 Classification for normed algebras 464; title: 3 Interlocation of subalgebras of a normed Boolean algebra 470; title: 4 Isomorphism between subalgebras 475; title: 5 Isomorphism of systems of subalgebras 531; title: 10. INDEPENDENCE 535; title: 1 A system of two subalgebras 535; title: 2 A test for metric independence 541.