Approximation by Continuous Potentials

Abstract

In this note we improve theorems in [1] and [2] dealing with approximation of (super)harmonic functions by continuous potentials. That is, we intend to show that for every finely open set G of a balayage space (X, W) there exists a continuous potential q ε P such that

$$S(G) = \overline {P + \mathbb{R}q} ,H(G) = \overline {H(q)}$$

.