Sokhet O. Approximately transitive transformation groups in the ergodic theory

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0499U002067

Thesis Registration Form

0499U002067.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

08-06-1999

Specialized Academic Board

Д 64.175.01

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

Essay

Approximately transitive (AT) transformation groups. 1) to find some sufficient conditions for approximate transitivity; 2) to describe AT actions via weak equivalence and product cocycles language; 3) to construct some examples. Nethods: ergodic theory, measure theory, theory of locally compact separable groups. Funny rank one implies AT; some sufficient conditions for AT are found; two theorems on induced actions, with corollaries; criterions of the AT property in terms of Mackey actions, product odometers, product cocycles and weak equivalence; examples.

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