Resumen de An analytic study on the self-similar fractals: differentiation of integrals

Miguel Reyes

• Let $E\subset\mathbb{R}^n$ be a self-similar fractal of Hausdorff dimension $s$, such that its Hausdorff measure $H^s$ is finite and positive. In this paper, we define two differentiation bases on $E$ which are density bases for $(E,H^s)$. For these differentiation bases, we study covering properties of Vitaly type, and we prove that they diffrentiate $L^1(E,H^s)$.