Ergodicity of a nonsingular transformation is equivalent to divergence of ergodic sums of all indicator functions of positive measure. In practice this divergence condition is easy to verify for “nice” sets and hard to verify for general sets. In this talk we will show two different arguments of how to pass from a statement on nice sets to general sets. The first gives a dynamical (non spectral) proof of a classical ergodicity criteria of Poisson suspensions and the second shows that a non-stationary Bernoulli shift under a natural distortion estimate is ergodic if and only if it is conservative. This is a joint work with E. Roy.
Tue, 09/01/2018 - 14:15 to 15:15