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Full Description
Boolean Algebras in Analysis consists of two parts. The first concerns the general theory at the beginner's level. Presenting classical theorems, the book describes the topologies and uniform structures of Boolean algebras, the basics of complete Boolean algebras and their continuous homomorphisms, as well as lifting theory. The first part also includes an introductory chapter describing the elementary to the theory.
The second part deals at a graduate level with the metric theory of Boolean algebras at a graduate level. The covered topics include measure algebras, their sub algebras, and groups of automorphisms. Ample room is allotted to the new classification theorems abstracting the celebrated counterparts by D.Maharam, A.H. Kolmogorov, and V.A.Rokhlin.
Boolean Algebras in Analysis is an exceptional definitive source on Boolean algebra as applied to functional analysis and probability. It is intended for all who are interested in new and powerful tools for hard and soft mathematical analysis.
Contents
0. Preliminaries on Boolean Algebras.- 1. The Basic Apparatus.- 2. Complete Boolean Algebras.- 3. Representation of Boolean Algebras.- 4. Topologies on Boolean Algebras.- 5. Homomorphisms.- 6. Vector Lattices and Boolean Algebras.- 7. Normed Boolean Algebras.- 8. Existence of a Measure.- 9. Structure of a Normed Boolean Algebra.- 10. Independence.- Appendices.- Prerequisites to Set Theory and General Topology.- 1 General remarks.- 2 Partially ordered sets.- 3 Topologies.- Basics of Boolean Valued Analysis.- 1 General remarks.- 2 Boolean valued models.- 3 Principles of Boolean valued analysis.- 4 Ascending and descending.- References.
