Regular Transition Functions and Regular Superprocesses

The class of regular Markov processes is very close to the class of right processes studied by Meyer, Getoor and others. We say that a transition function $p$ is regular if it is the transition function of a well-defined regular Markov process. A characterization of regular transition functions is given which implies that, if $p$ is regular, then the Dawson-Watanabe and the Fleming-Viot supertransition functions over $p$ belong to the same class.