Nearly hyperharmonic functions and Jensen measures

Abstract

In an abstact potential theoretic setting of balayage spaces, properties of nearly hyperharmonic functions are studied in detail. This is related to the study of strongly supermedian functions and Mertens' formula.

The results are applied to measurability problems of functionals defined by means of Jensen measures on harmonic spaces.

Keywords

• Jensen measure
• nearly hyperharmonic function
• strongly supermedian function