Abstract
We show that whenever the q-dimensional Minkowski content of a subset A ⊂ ℝd 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 ℝd, d ⩾ 3.
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This first author was supported by grants SVV 261315/2010 and GAČR 201/09/H012, the second author by grants MSM 0021620839 and GAČR 201/10/J039.
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Honzl, O., Rataj, J. Almost sure asymptotic behaviour of the r-neighbourhood surface area of Brownian paths. Czech Math J 62, 67–75 (2012). https://doi.org/10.1007/s10587-012-0017-6
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DOI: https://doi.org/10.1007/s10587-012-0017-6