SOME CALCULATIONS ON THE CONDITIONAL DENSITIES OF WELL-ADMISSIBLE MEASURES ON LINEAR-SPACES

When a probability measure m on a topological vector space E is well-a dmissible in a direction k is-an-element-of E, the conditional law in the direction k given the other directions is absolutely continuous wi th respect to the Lebesgue measure. We shall prove that its density fu nction is differentiable (in the sense precised below) and we shall ca lculate their derivatives. We give then two applications of such calcu lations.