On the Minkowski measurability of fractals

Falconer, K. J.

doi:10.1090/S0002-9939-1995-1224615-4

On the Minkowski measurability of fractals
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Proc. Amer. Math. Soc. 123 (1995), 1115-1124 Request permission

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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