Lebesgue points of functions in the complex Sobolev space

Abstract

Let [Formula: see text] be a function in the complex Sobolev space [Formula: see text], where [Formula: see text] is an open subset in [Formula: see text]. We show that the complement of the set of Lebesgue points of [Formula: see text] is pluripolar. The key ingredient in our approach is to show that [Formula: see text] for [Formula: see text] is locally bounded from above by a plurisubharmonic function.