We consider a proper submarkovian resolvent of kernels on a Lusin measurable space and a given excessive measure xi. With every quasi bounded excessive function we associate an excessive kernel and the corresponding Revuz measure. Every finite measure charging no xi-polar set is such a Revuz measure, provided the hypothesis (B) of Hunt holds. Under a weak duality hypothesis, we prove the Revuz formula and characterize the quasi boundedness and the regularity in terms of Revuz measures. We improve results of Azema [2] and Getoor and Sharpe [20] for the natural additive functionals of a Borel right process. [References: 27]
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