A Remark on Regularity of Excessive Functions for Certain Diffusions

Abstract

In an earlier paper [4], the first author has shown that a diffusion process whose potential kernel satisfies certain analytic conditions, has all of its excessive harmonic functions, which are not identically infinite, continuous. In a subsequent paper [5], the same author has shown that under these conditions the excessiveness of its nonnegative harmonic functions is automatic. In this paper we are showing that a regularity condition for the excessive functions introduced here, will imply that the Riesz measure does not charge the semi-polar sets of the process.