Note on Irregularities of Distribution Ii
نویسندگان
چکیده
THEOREM IB (Roth [11]). For every natural number N^2, there exists a distribution 0* of N points in U such that I. L-l \DL[&;B(y)]\dy«L(\ogN) u Note that Theorems 1A and IB remain true in the trivial case L = 1. Suppose now that ^ is a distribution of N points in the unit torus U = [0, 1)*, where K 5= 2. Let A be a compact and convex body in U. For any real number A € (0, 1], any proper orthogonal transformation r in U and any vector u e U, let
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