Krieger’s Finite Generator Theorem for Actions of Countable Groups I
نویسنده
چکیده
For an ergodic p.m.p. action G y (X,μ) of a countable group G, we define the Rokhlin entropy hRok G (X,μ) to be the infimum of the Shannon entropies of countable generating partitions. It is known that for free ergodic actions of amenable groups this notion coincides with classical Kolmogorov– Sinai entropy. It is thus natural to view Rokhlin entropy as a close analogue to classical entropy. Under this analogy we prove that Krieger’s finite generator theorem holds for all countably infinite groups. Specifically, if hRok G (X,μ) < log(k) then there exists a generating partition consisting of k sets.
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