On Milman's inequality and random subspaces which escape through a mesh in ℝn
Let S be a subset in the Euclidean space ℝn and 1 <- k < n. We find sufficient conditions which guarantee the existence and even with probability close to 1, of k-codimensional subspaces which miss S. As a consequence we derive a sharp form of Milman's inequality and discuss some applications to Banach spaces.
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