О регулярности условных вероятностей для случайных процессов

Let ($\Omega$, $\mathscr N$, $\mathbf P$) be a probability space, where $\Omega$ is the set of all right-continuous functions with left-hand side limits or the set of all continuous functions with values in a semicompact. For any $\sigma$-field $\mathscr H\subset\mathscr N$, the existence and uniqueness of a regular conditional probability distribution of $\mathbf P$ given $\mathscr H$ is proved.