is the limit of ergodic functions still ergodic? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T10:26:44Z http://mathoverflow.net/feeds/question/111473 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/111473/is-the-limit-of-ergodic-functions-still-ergodic is the limit of ergodic functions still ergodic? Mostafa 2012-11-04T16:36:01Z 2012-11-04T16:53:46Z <p>under what conditions is the limit of a sequence of ergodic functions still ergodic? are there simple counter-examples to this general statement?</p> http://mathoverflow.net/questions/111473/is-the-limit-of-ergodic-functions-still-ergodic/111477#111477 Answer by Pietro Majer for is the limit of ergodic functions still ergodic? Pietro Majer 2012-11-04T16:53:46Z 2012-11-04T16:53:46Z <p>A rotation $z\mapsto e^{2\pi i\alpha} z$ as a self-map of the unit circle is ergodic wrto the length measure iff $\alpha$ is irrational. So any sequence of irrational numbers converging to a rational number produces a counterexample.</p>