St. Petersburg Mathematical Society

Author(s): E. S. Dubtsov
Translated by: the author
Original publication: Algebra i Analiz, tom 19 (2007), nomer 2.
Journal: St. Petersburg Math. J. 19 (2008), 225-238.
MSC (2000): Primary 28A15, 28A75, 28A78, 42B35
Posted: 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

is large in the sense of the Hausdorff dimension.

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Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 28A15, 28A75, 28A78, 42B35

E. S. Dubtsov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: dubtsov@pdmi.ras.ru

DOI: 10.1090/S1061-0022-08-00995-3
PII: S 1061-0022(08)00995-3
Keywords: Regular singular measure, Hausdorff dimension, derivative
Received by editor(s): 31/AUG/2006
Posted: February 1, 2008
Additional Notes: This research was supported by RFBR (grant no.~05-01-00924).
Copyright of article: Copyright 2008, American Mathematical Society

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ISSN: 1547-7371(e) ISSN: 1061-0022(p)

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