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: settheoretical, topological and algebraic. Also, various combinations (e.g., algebraictopological) 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 quasiinvariant measures on solvable uncountable groups nonseparable extensions of invariant measures are constructed by using their ergodic components absolutely nonmeasurable additive functionals are constructed for certain classes of measures and, the structure of algebraic sums of measure zero sets is investigated. The material presented in this book is essentially selfcontained 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.
About Alexander Kharazishvili
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Author  :  Alexander Kharazishvili 
Publisher  :  Atlantis Press 
Data Published  :  31 May 2009 
ISBN  :  9078677201 
EAN  :  9789078677208 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  476 pages 
Age +  :  18 years 
Language  :  English 
Rating  : 
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