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Jan 27, 2014 at 5:57 comment added Anthony Quas @Klindsey: it's true that "most" IETs are uniquely ergodic. If you compose an IET with a rotation, of course you get another IET, so it's not completely unexpected that you should almost always get an ergodic transformation.
Jan 27, 2014 at 4:12 vote accept klindsey
Jan 27, 2014 at 4:12 comment added klindsey Thanks! Good point! In arxiv.org/abs/1210.5013, the authors prove that the answer to my question is "yes" in the case that $T$ is an interval exchange map. I wonder what it is about interval exchange maps that makes it true....
Jan 27, 2014 at 3:48 history answered Maurizio Monge CC BY-SA 3.0