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Sep 24, 2016 at 10:50 comment added m07kl @YemonChoi: I just want to indicate the converse implication. You can replace C(X) by a unital $C^*$-algebra $A$ and replace an invariant measure on $X$ by a $G$-invariant state on $ A$ to obtain a generalization.
Sep 22, 2016 at 19:41 comment added Yemon Choi Isn't this just a special case of @Ruy's answer?
Sep 22, 2016 at 17:14 history answered m07kl CC BY-SA 3.0