TOPICS IN MEASURE THEORY AND REAL ANALYSIS is popular PDF and ePub book, written by Alexander Kharazishvili in 2009-11-01, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, TOPICS IN MEASURE THEORY AND REAL ANALYSIS can be Read Online from any device for your convenience.
TOPICS IN MEASURE THEORY AND REAL ANALYSIS Book PDF Summary
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.
Detail Book of TOPICS IN MEASURE THEORY AND REAL ANALYSIS PDF
- Author : Alexander Kharazishvili
- Release : 01 November 2009
- Publisher : Springer Science & Business Media
- ISBN : 9789491216367
- Genre : Mathematics
- Total Page : 466 pages
- Language : English
- PDF File Size : 20,9 Mb
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