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Sets of Finite Perimeter and Geometric Variational Problems: An Introduction to Geometric Measure Theory by Francesco Maggi

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10

Rectifiable sets and blow-ups of Radon measures

We shall now introduce the notion of rectifiable set, which provides a generalization of the notion of surface of primary importance in the study of geometric variational problems. We start by fixing some terminology. Given kimages, 1 ≤ kn – 1, h ≥ 1, we shall say that M is a k-dimensional (embedded) surface of class Ch in imagesn (or a Ch-hypersurface when k = n – 1) if for every xM there exist an open neighborhood A of x, an open set Ek and a bijection f : EAM with fCh(E) and Jf > 0 ...

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