Boolean Algebras in Analysis

  • D. A. Vladimirov

Part of the Mathematics and Its Applications book series (MAIA, volume 540)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. General Theory of Boolean Algebras

    1. Front Matter
      Pages 1-1
    2. D. A. Vladimirov
      Pages 3-34
    3. D. A. Vladimirov
      Pages 35-81
    4. D. A. Vladimirov
      Pages 83-124
    5. D. A. Vladimirov
      Pages 125-179
    6. D. A. Vladimirov
      Pages 181-231
    7. D. A. Vladimirov
      Pages 233-276
    8. D. A. Vladimirov
      Pages 277-313
  3. Metric Theory of Boolean Algebras

    1. Front Matter
      Pages 315-315
    2. D. A. Vladimirov
      Pages 317-389
    3. D. A. Vladimirov
      Pages 391-444
    4. D. A. Vladimirov
      Pages 445-534
    5. D. A. Vladimirov
      Pages 535-561
  4. Back Matter
    Pages 563-604

About this book

Introduction

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.

Keywords

functional functional analysis set theory vector lattice

Authors and affiliations

  • D. A. Vladimirov
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-0936-1
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5961-1
  • Online ISBN 978-94-017-0936-1
  • About this book
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