In my course (see picture below) (under the formula (0.1.3)), they say that $p_{s,t}(x,dy)$ is a regular version of the conditional probability distribution of $X_t$ given $X_s$. Could someone tell me what does it mean ? Does is mean that $$\mathbb P\{X_t\in A\mid X_s=x\}=\int_A p_{s,t}(x,dy) \ ?$$
