Martingale ergodic and ergodic martingale processes with continuous time

In a paper dedicated to unifying martingales and ergodic averages, Kachurovskiǐ introduced certain unifying discrete-time martingale ergodic and ergodic martingale processes, for which he proved convergence theorems and established maximal and dominant inequalities. Our purpose in this article is to obtain similar results for such processes with continuous time. In addition, the results are used to assert convergence of yet another unifying process relating to Rota's approach to unification of martingales and Abel ergodic averages.
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