Boolean Algebras in Analysis

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Springer Science & Business Media, Apr 17, 2013 - Mathematics - 604 pages
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Boolean algebras underlie many central constructions of analysis, logic, probability theory, and cybernetics.

This book concentrates on the analytical aspects of their theory and application, which distinguishes it among other sources.

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.

 

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Contents

PRELIMINARIES ON BOOLEAN ALGEBRAS
3
THE BASIC APPARATUS
35
COMPLETE BOOLEAN ALGEBRAS
83
REPRESENTATION OF BOOLEAN ALGEBRAS
125
TOPOLOGIES ON BOOLEAN ALGEBRAS
181
HOMOMORPHISMS
233
VECTOR LATTICES AND BOOLEAN ALGEBRAS
277
NORMED BOOLEAN ALGEBRAS
317
EXISTENCE OF A MEASURE
391
STRUCTURE
445
INDEPENDENCE
535
Appendices 562
563
References
581
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