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Unformatted text preview: s is the Fourier transform
of the density for νn , which we already know converges uniformly on compact sets in R.
We conclude that νn,k has a radial density ρn,k with ρn,k (x) = ρn (x) and thus ρn,k converges
uniformly on compacts because any compact set is contained in a ball centered at the origin.
We are now ready for the main result. 2 6.2.3 Deﬁnition. A spherical cap centered at a ∈ S n−1 with radius r is
Ba (r) = {x ∈ S n−...
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 Spring '08
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 Geometry, Probability

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