On lattice structure of the space of pointwise limits of harmonic functions

Abstract

It is shown that the space of all pointwise limits of harmonic functions on an open set $U$ is a lattice in the natural ordering if and only if the set of all regular points of $U$ is an $F_\sigma$--set.

Keywords

• lattice
• structure
• space
• pointwise
• limits
• harmonic
• functions