  In this paper, we first use PDE techniques and probabilistic methods to
identify a kind of quasi-continuous random variables. Then we give a
characterization of the $G$-integrable processes and get a kind of
quasi-continuous processes by Krylov's estimates. This result is useful for the
development of $G$-stochastic analysis theory. Moreover, it also provides a
tool for the study of the non-Markovian It\^o processes.
