Derivatives of regular measures

Dubtsov, E.

doi:10.1090/S1061-0022-08-00995-3

Derivatives of regular measures
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by E. S. Dubtsov
Translated by: the author

St. Petersburg Math. J. 19 (2008), 225-238

DOI: https://doi.org/10.1090/S1061-0022-08-00995-3

Published electronically: February 1, 2008

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Abstract:

Let $\mu$ be a positive singular measure on Euclidean space. If $\mu$ is sufficiently regular, then for any $a\in [0, +\infty ]$ the set where the derivative of $\mu$ is equal to $a$ is large in the sense of the Hausdorff dimension.

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