| Foreword to the English Translation | |
| Denis Artem'evich Vladimirov (1929-1994) | |
| Preface | |
| Introduction | |
| Preliminaries on Boolean Algebras | p. 3 |
| Lattices | p. 3 |
| Boolean algebras | p. 10 |
| Additive functions on Boolean algebras. Measures. Relation to probability theory | p. 23 |
| Automorphisms and invariant measures | p. 29 |
| The Basic Apparatus | p. 35 |
| Subalgebras and generators | p. 35 |
| The concepts of ideal, filter, and band | p. 48 |
| Factorization, homomorphisms, independence, and free Boolean algebras | p. 55 |
| Complete Boolean Algebras | p. 83 |
| Complete Boolean algebras; their subalgebras and homomorphisms | p. 83 |
| The exhaustion principle and the theorem of solid cores | p. 89 |
| Construction of complete Boolean algebras | p. 95 |
| Important examples of complete Boolean algebras | p. 102 |
| The Boolean algebra of regular open sets | p. 103 |
| The type, weight, and cardinality of a complete Boolean algebra | p. 105 |
| Structure of a complete Boolean algebra | p. 111 |
| Representation of Boolean Algebras | p. 125 |
| The Stone Theorem | p. 125 |
| Interpretation of the basic notions of the theory of Boolean algebras in the language of Stone spaces | p. 136 |
| Stone functors | p. 150 |
| Topologies on Boolean Algebras | p. 181 |
| Directed sets and generalized sequences | p. 181 |
| Various topologies on Boolean algebras | p. 184 |
| Regular Boolean algebras. Various forms of distributivity | p. 223 |
| Homomorphisms | p. 233 |
| Extension of homomorphisms | p. 234 |
| Lifting | p. 238 |
| Extension of continuous homomorphisms | p. 244 |
| Again on representation of a Boolean algebra | p. 267 |
| Vector Lattices and Boolean Algebras | p. 277 |
| K-spaces and the related Boolean algebras | p. 277 |
| Spectral families and resolutions of the identity. Spectral measures | p. 287 |
| Separable Boolean algebras and [sigma]-algebras of sets. Measurable functions | p. 296 |
| The integral with respect to a spectral measure and the Freudenthal Theorem. The space [actual symbol not reproducible] as the family of resolutions of the identity. Functions of elements | p. 298 |
| Normed Boolean Algebras | p. 317 |
| Normed algebras | p. 317 |
| Extension of a countably additive function. The Lebesgue - Caratheodory Theorem | p. 325 |
| NBAs and the metric structures of measure spaces | p. 332 |
| Totally additive functions and resolutions of the identity of a normed algebra | p. 342 |
| Subalgebras of a normed Boolean algebra | p. 353 |
| Fundamental systems of partitions | p. 382 |
| Systems of measures and the Lyapunov Theorem | p. 387 |
| Existence of a Measure | p. 391 |
| Conditions for existence of a measure | p. 391 |
| Existence of a measure invariant under the automorphism group | p. 399 |
| The Potepun Theorem | p. 417 |
| Automorphisms of normable algebras and invariant measures | p. 433 |
| Construction of a normed Boolean algebra given a transformation group | p. 439 |
| Structure of a Normed Boolean Algebra | p. 445 |
| Structure of a normed algebra | p. 445 |
| Classification for normed algebras | p. 464 |
| Interlocation of subalgebras of a normed Boolean algebra | p. 470 |
| Isomorphism between subalgebras | p. 475 |
| Isomorphism of systems of subalgebras | p. 531 |
| Independence | p. 535 |
| A system of two subalgebras | p. 535 |
| A test for metric independence | p. 541 |
| App. :Prerequisites to Set Theory and General Topology | p. 563 |
| App.: Basics of Boolean Valued Analysis | p. 569 |
| References | p. 581 |
| Index | p. 601 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
