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On the Minkowski measurability of fractals


Author: K. J. Falconer
Journal: Proc. Amer. Math. Soc. 123 (1995), 1115-1124
MSC: Primary 28A80
DOI: https://doi.org/10.1090/S0002-9939-1995-1224615-4
MathSciNet review: 1224615
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Abstract: This note addresses two aspects of Minkowski measurability. First we present a short "dynamical systems" proof of the characterization of Minkowski measurable compact subsets of $ \mathbb{R}$. Second, we use a renewal theory argument to point out that "most" self-similar fractals are Minkowski measurable and calculate their Minkowski content.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1224615-4
Article copyright: © Copyright 1995 American Mathematical Society

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