Introduction

Abstract

The developments in the recent years of the potential theory emphasized a class of functions larger than that of excessive functions (i.e. the positive superharmonic functions from the classical potential theory associated with the Laplace operator), namely the strongly supermedian functions. It turns out that a positive Borel function will be strongly supermedian if and only if it is the infimum of all its excessive majorants. Apparently, these functions have been introduced by J.F. Mertens and then they have been studied mainly by P.A. Meyer, G. Mokobodzki, D. Feyel and recently by P.J. Fitzsimmons and R.K. Getoor.