New contributions on the Potential Theory

The development of potential theory has highlighted the importance of a class of functions, called class of excessive functions. This was studied by P.A. Meyer, G. Mokobodzki, N. Boboc, Gh. Bucur, L. Beznea, etc. If has been shown that by giving a proper sub-Markovian proper resolvent on a measurable space the set of excessive measures on this space forms a H-cone. We put conditions on a H-cone of a positive measures on a Lusin measurable space to exists a resolvent of kernels on this space such that this H-cone is equals with a H-cone of excessive measures. This work should be useful to professionals in Mathematical Analysis, to those involved in the Potential Theory, a research field still open for new developments.