Superharmonic Functions Outside Negligible Sets

A study of quasi superharmonic functions in Brelot spaces is intro-duced. A characterization of quasi superharmonic functions, in Brelot spaces, in terms of harmonic and finely harmonic measures is given. We prove that a Borel function is quasi superharmonic function if and only if it is a lower envelope of a class of superharmonic functions. Mathematics Subject Classification: Primary 31B05, Secondary 31D05