Quasi superharmonic functions in Brelot spaces

The concept of quasi superharmonic function, in terms of Jensenmeasures, in Brelot spaces is introduced. A characterization of quasisuperharmonic functions in Brelot spaces in terms of harmonic measuresis given. We show that a lower semicontinuous regularization of a quasisuperharmonic function is superharmonic function. Moreover, we showthat a quasi superharmonic function in Brelot spaces equals to its lowersemicontinuous regularization out side of a polar set.