On some results concerning the reduite and balayage

If J is an analytic, saturated gambling house with compact sections, and mu less than or equal to lambda, we show that there exists a (submarkovian) b orel kernel P permitted in J such that mu = lambdaP. If nu = (V-alpha)(alph a >0) is a proper submarkovian resolvent on a Lusin space X, we study the r egularity of the reduite R-s(A) of an excesive function s on a set A subset of X.