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arXiv · 1203.4221

Tangent measures of typical measures

Tuomas Sahlsten
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Abstract

We prove that for a typical Radon measure mu in R^d, every non-zero Radon measure is a tangent measure of mu at mu almost every point. This was already shown by T. O'Neil in his PhD thesis from 1994, but we provide a different self-contained proof for this fact. Moreover, we show that this result is sharp: for any non-zero measure we construct a point in its support where the set of tangent measures does not contain all non-zero measures. We also study a concept similar to tangent measures on trees, micromeasures, and show an analogous typical property for them.

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Tuomas Sahlsten. 2014-12-01. Tangent measures of typical measures. https://arxiv.org/abs/1203.4221

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