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Discrepancies and their means

Published 4 Sep 2023 in math.CA and math.CO | (2309.01547v1)

Abstract: It is shown that the discrepancy function for point distributions on a torus is expressed by an explicit formula in terms of its mean values on sub-tori. As an application of this formula, a simple proof of a theorem of Lev on the equivalence of $L_{\infty}$- and shifted $L_q$-discrepancies is given.

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