... view of these results and examples, the problem arises of finding min-imal additional assumptions to (1.6) ensuring the equivalence (up to transla-tions) of E and Es. These are elucidated in Theorem ... Hmstands for the outer m-dimensional Hausdorff measure. As-sumption (1.9), of geometric nature, turns out to be equivalent to the vanishing of the perimeter of Esrelative to cylinders, of zero Lebesgue ... R)=∂∗Es∩(B×R)dHn−1=Bdx(∂∗Es)xdH0(y)|νEsy(x,y)|(3.17)=GE∩Bdx(∂∗Es)xdH0(y)|νEsy(x,y)|=GE∩Bdx(∂∗Es)x1+n−1i=1νEsi(x,y)νEsy(x,y)2dH0(y),where the first equality is due to (2.9), the second to Theorem F (which wemay apply since we are assuming that B ⊂ GEs), the third to the fact thatLn−1(π(E)+\ GE) = 0, and the fourth to...