Let O(X) be the metric space of all compact subsets of a compact set X in Rn and let L be an element of O(X). Let vol(L) be the volume of L. How do we prove that vol(L) is a continuous function on O(X)?
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closed as off topic by Bill Johnson, Goldstern, Andreas Blass, Chris Godsil, Misha May 12 '13 at 22:51
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It depends on the metric you use on $O(X)$. I guess the Hausdorff one? 

