  In this article, we show that a function $f\in M^{s,p}(X),$ $0<s\leq 1,$
$0<p<1,$ 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 $h.$
