Slow Convergences of Ergodic Averages

Birkhoff's theorem asserts that, for an ergodic automorphism, time averages converge to the space average. Krengel showed that, for a given sequence $\psi(n)\to+0$ and any ergodic automorphism, there exists an indicator function such that the corresponding time means converge a.e. slower than $\psi$. We give a new proof of the absence of estimates for rates of convergence, answering a question of Podvigin.