I have the following problem,
Given that $B_t$ is a Brownian motion starting at $x$, and $f$ is a continuous and bounded function. Define that,
$P_tf(x)=\mathbb{E}[f(B_t)]$.
For any $s,t>0$, I want to show the Chapman Kolgomorov rule, i.e.
$P_{s+t}f(x)=P_t(P_sf)(x)$.
Thanks in advance.