MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

under what conditions is the limit of a sequence of ergodic functions still ergodic? are there simple counter-examples to this general statement?

share|cite|improve this question
up vote 13 down vote accepted

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.