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Sep 20, 2013 at 11:44 comment added Asaf @Fry, see Def 1. p. 9 , and Bourgain's conjecture in p. 6 and the top theorem in p.6 (Bourgain-Glibichuk-Konyagin), although the cases of Bourgain's theorem are dealing with the example that Marc posted, more than the general "ergodic theorem" you're asking for. Another instance in theorem 6 in p.14 (which I've referenced in my answer as (3)).
Sep 20, 2013 at 8:57 comment added user40023 Unfortunately, the survey of Lindenstrauss does not contain any definition of equidistribution similar to the one I posted.
Sep 12, 2013 at 15:31 history answered Marc Palm CC BY-SA 3.0