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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Derivatives of regular measures


Author: 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
Published electronically: February 1, 2008
MathSciNet review: 2333898
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

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: http://dx.doi.org/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): August 31, 2006
Published electronically: February 1, 2008
Additional Notes: This research was supported by RFBR (grant no. 05-01-00924).
Article copyright: © Copyright 2008 American Mathematical Society