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

Autores: Miguel Reyes
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 40, Fasc. 2, 1989, págs. 159-167
Idioma: inglés
Títulos paralelos:
- Un estudio analítico sobre fractales autosimilares: diferenciación de integrales
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Resumen
- 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 $L^1(E,H^s)$.