English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

For an ergodic p.m.p. action \(G \curvearrowright (X, \mu )\) of a countable group G, we define the Rokhlin entropy \(h^{\mathrm {Rok}}_G(X, \mu )\) 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 \(h^{\mathrm {Rok}}_G(X, \mu ) < \log (k)\) then there exists a generating partition consisting of k sets.

Krieger’s finite generator theorem for actions of countable groups I