  Birkhoff's theorem states that for an ergodic automorphism, the time averages
converge to the space average. Given sequence $\psi(n)\to+0$, U. Krengel proved
that for any ergodic automorphism there is an indicator such that the
corresponding time averages converged a.e. with a rate slower than $\psi$. We
prove again similar statements answering a question of I. Podvigin in passing.
