Asymptotics of the s-fractional Gaussian perimeter as $$s\rightarrow 0^+$$

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