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We prove that a topologically predictable action of a countable amenablegroup has zero topological entropy, as conjectured by Hochman. On route, weinvestigate invariant random orders and formulate a unified Kieffer-Pinskerformula for the Kolmogorov-Sinai entropy of measure preserving actions ofamenable groups. We also present a proof due to Weiss for the fact thattopologically prime actions of sofic groups have non-positive topological soficentropy.

Predictability, topological entropy and invariant random orders