Atlantis Studies in Mathematics

TOPICS IN MEASURE THEORY AND REAL ANALYSIS

Authors: Kharazishvili, Alexander

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About this book

This book highlights various topics on measure theory and vividly demonstrates that the different questions of this theory are closely connected with the central measure extension problem. Several important aspects of the measure extension problem are considered separately: set-theoretical, topological and algebraic. Also, various combinations (e.g., algebraic-topological) of these aspects are discussed by stressing their specific features. Several new methods are presented for solving the above mentioned problem in concrete situations. In particular, the following new results are obtained: the measure extension problem is completely solved for invariant or quasi-invariant measures on solvable uncountable groups; non-separable extensions of invariant measures are constructed by using their ergodic components; absolutely non-measurable additive functionals are constructed for certain classes of measures; the structure of algebraic sums of measure zero sets is investigated. The material presented in this book is essentially self-contained and is oriented towards a wide audience of mathematicians (including postgraduate students). New results and facts given in the book are based on (or closely connected with) traditional topics of set theory, measure theory and general topology such as: infinite combinatorics, Martin's Axiom and the Continuum Hypothesis, Luzin and Sierpinski sets, universal measure zero sets, theorems on the existence of measurable selectors, regularity properties of Borel measures on metric spaces, and so on. Essential information on these topics is also included in the text (primarily, in the form of Appendixes or Exercises), which enables potential readers to understand the proofs and follow the constructions in full details. This not only allows the book to be used as a monograph but also as a course of lectures for students whose interests lie in set theory, real analysis, measure theory and general topology.

Table of contents (20 chapters)

  • The problem of extending partial functions

    Kharazishvili, Alexander B.

    Pages 1-18

  • Some aspects of the measure extension problem

    Kharazishvili, Alexander B.

    Pages 19-37

  • Invariant measures

    Kharazishvili, Alexander B.

    Pages 39-62

  • Quasi-invariant measures

    Kharazishvili, Alexander B.

    Pages 63-78

  • Measurability properties of real-valued functions

    Kharazishvili, Alexander B.

    Pages 79-96

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-94-91216-36-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
TOPICS IN MEASURE THEORY AND REAL ANALYSIS
Authors
Series Title
Atlantis Studies in Mathematics
Series Volume
2
Copyright
2009
Publisher
Atlantis Press
Copyright Holder
Atlantis Press and the authors
eBook ISBN
978-94-91216-36-7
DOI
10.2991/978-94-91216-36-7
Series ISSN
1875-7634
Edition Number
1
Number of Pages
XI, 461
Topics