We study the asymptotic behaviour of the renormalised s-fractional Gaussian perimeter of a set E inside a domain \(\Omega \) as \(s\rightarrow 0^+\). Contrary to the Euclidean case, as the Gaussian measure is finite, the shape of the set at infinity does not matter, but, surprisingly, the limit set function is never additive.

中文翻译：

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s-分数高斯周长的渐近线为 $$s\rightarrow 0^+$$ s → 0 +

我们研究域\(\Omega \)内的集合E的重整化s -分数高斯周长的渐近行为为\(s\rightarrow 0^+\)。与欧几里得的情况相反，由于高斯测度是有限的，所以无穷大集合的形状无关紧要，但令人惊讶的是，极限集合函数永远不会是加法的。