Generalized Lebesgue points for Sobolev functions

Abstract

In this article, we show that a function $f\in M^{s,p}(X),$ $0<s\le 1,$ $0<p<1,$ where $X$ is a doubling metric measure space, has generalized Lebesgue points outside a set of ${\mathcal{H}}^h$-Hausdorff measure zero for a suitable gauge function $h.$

10 pages