Differentiation properties of class $L^1([0,1{]}^2)$ with respect to two different basis of rectangles

Michihiro Hirayama, Davit Karagulyan

It is a well-known result by Saks \cite{Saks1934} that there exists a function $f\in L^1({\mathbb{R}}^2)$ so that for almost every $(x,y)\in {\mathbb{R}}^2$ \[ \lim_{\substack{\mathrm…