For tame flows, Haar measure on an Ellis group decompresses to a regular measure on the enveloping semigroup, and the enveloping flow is amenable iff the original flow is hereditarily amenable.
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Haar decompression and amenability of Ellis flows
For tame flows, Haar measure on an Ellis group decompresses to a regular measure on the enveloping semigroup, and the enveloping flow is amenable iff the original flow is hereditarily amenable.