Zero-One law for the rates of convergence in the Birkhoff ergodic theorem with continuous time

We consider monotone pointwise estimates of the rates of convergence in the Birkhoff ergodic theorem with continuous time. For an ergodic semiflow in a Lebesgue space, we prove that such estimates hold either on a null or full measure set. It is shown that monotone estimates that are true almost everywhere always exist. We study the lattice of such estimates and also consider some questions on their unimprovability.