A martingale ergodic theorem

We prove the martingale ergodic theorem of Kachurovskii which unifies ergodic theorems and theorems on the convergence of martingales, without using the previously required additional integrability condition for the supremum of the process. This condition is replaced by the commutation condition on the conditional expectation and ergodic averaging operators, which for automorphisms is equivalent to the invariance condition on the filtration; meanwhile, the unification remains valid.