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The $$L_p$$ L p metrics, extensions of the Hausdorff metric for convex bodies, were investigated by Vitale in 1985. In this paper, we extend $$L_p$$ L p metrics to Orlicz metrics, and show that these Orlicz metrics generate the same topology as the Hausdorff one in the space of all convex bodies (i.e., non-empty compact convex subsets), consequently, the space of all convex bodies...
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