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Sep 23, 2014 at 14:24 comment added Julian Newman Sorry for the late response. Thank you very much for the above information about unique ergodicity, I hadn't been aware of this theorem, and it looks quite nice. Now it seems that you may have perhaps misunderstood my question, seeing as you said that in the case of unique ergodicity, the "result I am looking for" follows by Birkhoff's ergodic theorem. If I already have unique ergodicity then ergodic decomposition is a tautology and has nothing to do with Birkhoff's ergodic theorem; the whole point of ergodic decomposition is for cases where I might not have unique ergodicity.
Sep 2, 2014 at 6:46 history edited Davide Giraudo CC BY-SA 3.0
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Sep 2, 2014 at 5:38 history answered Sergio Almada CC BY-SA 3.0