Lecture #10 Notes

624 theorem levy if a s n1 t 0 and b ba r with

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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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