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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