Tangent measures of typical measures

Tuomas Sahlsten

    Research output: Contribution to journalArticlepeer-review


    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
    Pages (from-to)53-80
    Number of pages28
    JournalReal Analysis Exchange
    Issue number1
    Publication statusPublished - 2015


    • math.CA
    • 28A12, 28A75, 28A80
    • Cubes
    • Tangents
    • Mathematical theorems


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