countable monographs equivalence mathematical

books:

Rigidity Theorems For Actions Of Product Groups And Countable Borel Equivalence Relations (Memoirs of the ...
Greg Hjorth, Alexander S. Kechris

American Mathematical Society, 2005

This memoir is both a contribution to the theory of Borel equivalence relations, considered up to Borel reducibility, and measure preserving group actions considered up to orbit equivalence. Here $E$ is said to be Borel reducible to $F$ if there is a Borel function $f$ with $x E y$ if and only if $f(x) F f(y)$. Moreover, $E$ is orbit equivalent to $F$ if the respective measure spaces equipped with the extra structure provided by the equivalence ...

Classification and Orbit Equivalence Relations (Mathematical Surveys and Monographs)
Greg Hjorth

American Mathematical Society, 1999

Actions of Polish groups are ubiquitous in mathematics. In certain branches of ergodic theory and functional analysis, one finds a systematic study of the group of measure-preserving transformations and the unitary group. In logic, the analysis of countable models intertwines with results concerning the actions of the infinite symmetric group. This text develops the theory of Polish group actions entirely from scratch, ultimately presenting a ...