Décomposition d'une théorie du potentiel en des sous-espaces elliptiques et paraboliques

Let V be a proper kernel on a measurable space (X, ℬ), and ℰV the cone of excessive functions generated by V. We give a necessary and sufficient condition to decompose the space (X, ℰV) in an ordered and countable family of subspaces (Xn, ℰVn), which are elliptic or parabolic. The Xi's are finely open and measurable and form a partition of X. The kernel W = ∑ Vi on ∑ Xi is subordinate to V, and has a triangular matrix. © 2000 Kluwer Academic Publishers.