In the frame of Borel right Markov processes, we investigate,
following an analytical point of view, the Revuz correspondence between classes
of potential kernels and their associated measures, improving upon the results
of Revuz, Azéma, Getoor and Sharpe, Fitzsimmons, Fitzsimmons and Getoor
and Dellacherie, Maisonneuve and Meyer. In the probabilistic approach of the
problem, the kernels that occur are the potential operators of different types
of homogeneous random measures. We completely characterize the hypothesis
(B) of Hunt in terms of Revuz measures.