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 . 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