May 10, 2008 with 0 < p < 1 is not locally convex
This is impossible because 0 < p < 1. /// For contrast, to prove the triangle inequality for the alleged metric on ‘p with 0 < p < 1, it suffices to prove that (x+y)p < xp +yp (for 0 < p < 1 and x,y ≥ 0) To this end, take x ≥ y. By the mean value theorem, (x+y)p ≤ xp +pξp−1y (for some x ≤ ξ ≤ x+y) and ................
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