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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A measure with a large set of tangent measures

Author: Toby O’Neil
Journal: Proc. Amer. Math. Soc. 123 (1995), 2217-2220
MSC: Primary 28A75
MathSciNet review: 1264826
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Abstract: There exists a Borel regular, finite, non-zero measure $ \mu $ on $ {\mathbb{R}^d}$ such that for $ \mu $-a.e. x the set of tangent measures of $ \mu $ at x consists of all non-zero, Borel regular, locally finite measures on $ {\mathbb{R}^d}$.

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  • [1] David Preiss, Geometry of measures in 𝑅ⁿ: distribution, rectifiability, and densities, Ann. of Math. (2) 125 (1987), no. 3, 537–643. MR 890162, 10.2307/1971410
  • [2] Pertti Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge Studies in Advanced Mathematics, vol. 44, Cambridge University Press, Cambridge, 1995. Fractals and rectifiability. MR 1333890

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Article copyright: © Copyright 1995 American Mathematical Society