Feyel's techniques on the supermedian functionals and strongly supermedian functions (Q1300176)

Based on some of their earlier results, the authors extend techniques and results of \textit{D. Feyel} [Z. Wahrsch. verw. Geb. 58, 183-198 (1981; Zbl 0475.60059) and Bull. Soc. Math. Fr. 111, 41-57 (1983; Zbl 0562.31012)] to the case of a submarkovian resolvent of kernels on a Lusin measurable space. This framework covers the situation of a general right Markov process. Among the results established in this paper, let us mention: the representation of \(\theta \)-supermedian functionals as \(\theta \)-strongly supermedian functions, an essential improvement of the quasi Lindelöf property for the fine topology, a Mertens-type decomposition for \(\theta \)-strongly supermedian functions, quasi continuity results for strongly supermedian functions.