Local conical dimensions for measures

Abstract

We study the decay of $\mu (B(x,r)\cap C)/\mu (B(x,r))$ as $r\downarrow 0$ for different kinds of measures $\mu$ on ${\mathbb{R}}^n$ and various cones $C$ around $x$. As an application, we provide sufficient conditions implying that the local dimensions can be calculated via cones almost everywhere.

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Cited by in corpus (1)

• Dynamics of the scenery flow and geometry of measures