A measure with a large set of tangent measures
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- by Tacey O’Neil
- Proc. Amer. Math. Soc. 123 (1995), 2217-2220
- DOI: https://doi.org/10.1090/S0002-9939-1995-1264826-5
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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 ${\mathbb {R}^d}$.References
- David Preiss, Geometry of measures in $\textbf {R}^n$: distribution, rectifiability, and densities, Ann. of Math. (2) 125 (1987), no. 3, 537–643. MR 890162, DOI 10.2307/1971410
- 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, DOI 10.1017/CBO9780511623813
Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2217-2220
- MSC: Primary 28A75
- DOI: https://doi.org/10.1090/S0002-9939-1995-1264826-5
- MathSciNet review: 1264826