Article
MSC:
28A75,
52A20,
52A38,
60D05,
60J65 | MR 2899735 | Zbl 1249.28003 | DOI: 10.1007/s10587-012-0017-6
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Keywords:
Minkowski content; Kneser function; Brownian motion; Wiener sausage
Minkowski content; Kneser function; Brownian motion; Wiener sausage
Summary:
We show that whenever the $q$-dimensional Minkowski content of a subset $A\subset \mathbb R^d$ exists and is finite and positive, then the “S-content” defined analogously as the Minkowski content, but with volume replaced by surface area, exists as well and equals the Minkowski content. As a corollary, we obtain the almost sure asymptotic behaviour of the surface area of the Wiener sausage in $\mathbb R^d$, $d\geq 3$.
References:
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