Feller semigroup
= Feller semigroup
{c}
{title2=$P_t1=1,\quad f\geq0\Longrightarrow P_tf\geq0$}
On a compact <metric space>, a conservative Feller semigroup is a <strongly continuous semigroup> of positive unital operators on $C(X)$. The <Riesz-Markov-Kakutani representation theorem> associates a <Markov kernel> to each operator. On noncompact spaces the standard definition uses $C_0(X)$; conservativity then refers to the corresponding kernels having mass one, even when $1\notin C_0(X)$.