On some results concerning the reduite and balayage (Q2718019)

The paper presents improvements of some results of Cartier, Strassen and Beznea-Boboc, concerning the theory of reduite and balayage in potential theory. The framework is that of gambling houses as developed by Dellacherie-Meyer (for the ``discrete'' case) and then the ``continuous'' frame given by a proper submarkovian resolvent. Both probabilistic and analytic tools are used. NEWLINENEWLINENEWLINESpecifically, if \(J\) is an analytic, saturated gambling house with compact sections and \(\mu \leq J \nu \), it is proved that there exists a submarkovian, borel kernel \(P\), permitted in \(J\), such that \(\mu = \nu P\). In the continuous case, the regularity of the reduite \(R_{s}^{A}\) of an excessive function on the set \(A\) is studied.