On Choquet's dichotomy of capacity for Markov processes (Q1184092)

Following Choquet, the capacity associated with a Markov process is said to be dichotomous if each compact set \(K\) contains two disjoint sets with the same capacity as \(K\). The authors prove the following two items: 1. In the context of right processes, the dichotomy of capacity is equivalent to Hunt's hypothesis that semipolar sets are polar. 2. A weaker form of the dichotomy is valid for any Lévy process with absolutely continuous potential kernel.