Strongly supermedian kernels and Revuz measures

In the frame of Borel right Markov processes, we investigate, following an analytical point of view, the Revuz correspondence between classes of poten tial kernels and their associated measures, improving upon the results of R evuz, Azema, Getoor and Sharpe, Fitzsimmons, Fitzsimmons and Getoor and Del lacherie, Maisonneuve and Meyer. In the probabilistic approach of the probl em, the kernels that occur are the potential operators of different types o f homogeneous random measures. We completely characterize the hypothesis (B ) of Hunt in terms of Revuz measures.