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Mar 25, 2020 at 20:10 vote accept A. Ninno
Mar 25, 2020 at 20:10 comment added A. Ninno Thank you very much! For convenience of future readers i add that the same argument that you presented works with the compactness of the sets of finite perimeter: that is If $\{ E_h\}_h$ are of finite perimeter and they satisfies $sup_h P(E_h)<\infty$ and $E_h\subset B_R$ for a certain R Then there exists $E$ a set of finite perimeter s.t. $E_h\to E$ and $\mu_{E_h}\to^{\star}\mu_E$.
Mar 25, 2020 at 19:37 history answered Kostya_I CC BY-SA 4.0