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arXiv · 1204.5886

Local conical dimensions for measures

De-Jun Feng·Antti Käenmäki·Ville Suomala
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Abstract

We study the decay of $μ(B(x,r)\cap C)/μ(B(x,r))$ as $r\downarrow 0$ for different kinds of measures $μ$ on $\R^n$ 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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De-Jun Feng, Antti Käenmäki, Ville Suomala. 2012-04-26. Local conical dimensions for measures. https://doi.org/10.1017/s0305004113000066

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