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arXiv · 2309.01547

Discrepancies and their means

M. M. Skriganov
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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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M. M. Skriganov. 2023-09-04. Discrepancies and their means. https://arxiv.org/abs/2309.01547

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