Let X be a cadlag Markov process with separable metric state space S, governed by semigroup of transition kernels (N_{t})_{t≥0}. Let f be a bounded, non-negative, continuous function on S^{2}, vanishing in a uniform neighbourhood of the diagonal. Define
and suppose that sup{|J_{t}f(x)|: t>0, x εS}<∞ and that
exists for each xεS. Then
du for each t≥0 and each xεS.