On amarts with continuous time

We introduce a notion of a $D_v$-amart into consideration, which generalizes a notion of a martingale. For stochastic processes $(X_t(\omega))_{t\ge 0}$, which are $D_v$-amarts, we obtain sample properties of their trajectories such as the existence of
$$ \lim_{t\uparrow\tau(\omega)}X_t(\omega), \qquad \lim_{t\downarrow\tau(\omega)}X_t(\omega), $$
where $\tau=\tau(\omega)$ are some or other stopping times, and the existence of modifications with right-continuous trajectories.