Tangent measures of typical measures

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Abstract

We prove that for a typical Radon measure μ in ℝd, every non-zero Radon measure is a tangent measure of μ at μ almost every point. This was already shown by T. O'Neil in his Ph.D. 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. Mathematical Reviews subject classification: Primary: 28A12; Secondary: 28A75, 28A80 Key words: tangent measures, Baire category
Original languageEnglish
JournalREAL ANALYSIS EXCHANGE
Publication statusPublished - 2015
MoE publication typeA1 Journal article-refereed

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