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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 subMarkovian proper resolvent on a measurable space the set of excessive measures on this space forms a Hcone. We put conditions on a Hcone of a positive measures on a Lusin measurable space to exists a resolvent of kernels on this space such that this Hcone is equals with a Hcone 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.
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