Geodesic
Bounds for the average \(L^p\)-extreme and the \(L^\infty\)-extreme discrepancy
The electronic journal of combinatorics, Tome 12 (2005)
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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.
DOI : 10.37236/1951
Classification : 11K38
Mots-clés : discrepancy, geometric discrepancy, star discrepancy 
@article{10_37236_1951,
     author = {Michael Gnewuch},
     title = {Bounds for the average {\(L^p\)-extreme} and the {\(L^\infty\)-extreme} discrepancy},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1951},
     zbl = {1096.11029},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1951/}
}
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UR  - http://geodesic.mathdoc.fr/articles/10.37236/1951/
DO  - 10.37236/1951
ID  - 10_37236_1951
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%0 Journal Article
%A Michael Gnewuch
%T Bounds for the average \(L^p\)-extreme and the \(L^\infty\)-extreme discrepancy
%J The electronic journal of combinatorics
%D 2005
%V 12
%U http://geodesic.mathdoc.fr/articles/10.37236/1951/
%R 10.37236/1951
%F 10_37236_1951
Michael Gnewuch. Bounds for the average \(L^p\)-extreme and the \(L^\infty\)-extreme discrepancy. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1951

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