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Let {x k,n } n k=1 and {x k,n+1 } n+1 k=1 , n ∈ N, be two given sets of real distinct points with x 1,n+1 < x 1,n < x 2,n+1 < · · · < x n,n < x n+1,n+1. Wendroff (cf. [3]) proved that if p n (x) = n k=1 (x − x k,n) and p n+1 (x) = n+1 k=1 (x − x k,n+1) then p n and p n+1 can be embedded in a non-unique infinite monic orthogonal sequence {p n } ∞ n=0. We… (More)

is obtained by slicing off each " corner " D i of the simplex n at the midpoint of each edge. But each D i is actually similar to n by a scaling factor of 1/2, so it has measure (1/2) n−1 times the measure of n. Therefore, µ(ϒ n) = µ(n) − n(1/2) n−1 µ(n) = [1 − n(1/2) n−1 ]µ(n), and the theorem follows. Readers interested in geometric probability might want… (More)

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