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 22:51Questions on MathOverflow are expected to relate to research level mathematics within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here. If this question can be reworded to fit the rules in the help center, please edit the question. 


It depends on the metric you use on $O(X)$. I guess the Hausdorff one? 

