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ASYMPTOTICS OF THE s -PERIMETER AS s (cid:38) 0

. We deal with the asymptotic behavior of the s -perimeter of a set E inside a domain Ω as s (cid:38) 0. We prove necessary and suﬃcient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of E and Ω. Moreover, we construct examples of sets for which the limit does not exist.