Local Hausdorff Measure

John Dever

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arXiv · 1610.00078

Local Hausdorff Measure

John Dever

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Abstract

A local Hausdorff dimension is defined on a metric space. We study its properties and use it to define a local Hausdorff measure. We show that in the case that in the local Hausdorff measure is finite we can recover the global Hausdorff dimension from the local one. Lastly, for a variable Ahlfors Q-regular measure on a compact metric space, we show the Ahlfors regular measure is strongly equivalent to the local Hausdorff measure and that the function $Q$ is equal to the local Hausdorff dimension.

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John Dever. 2016-10-01. Local Hausdorff Measure. https://arxiv.org/abs/1610.00078

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