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{\bf Michael Gnewuch }
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{\bf Bounds for the Average $L^p$-Extreme and the $L^\infty$-Extreme Discrepancy}
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The extreme or unanchored discrepancy is the geometric discrepancy of
point sets in the $d$-dimensional unit cube with respect to the set
system of axis-parallel boxes. For $2\leq p < \infty$ we provide upper
bounds for the average $L^p$-extreme discrepancy.  With these bounds
we are able to derive upper bounds for the inverse of the
$L^\infty$-extreme discrepancy with optimal dependence on the
dimension $d$ and explicitly given constants.

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