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We have that A is non empty and compact.

We show An converges to A in the Hausdorff metric (D).

I know D(A,B)= Inf {t>or eq.0 : A C B_t and B C A_t} Where A_t is the t-parallel body of A meaning A_t={x in X: d(x,A) < or eq.t}.

But I am not sure how to proceed.