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Modified Schmidt games and Diophantine approximation with weights
Journal article   Open access   Peer reviewed

Modified Schmidt games and Diophantine approximation with weights

Dmitry Kleinbock and Barak Weiss
Advances in mathematics (New York. 1965), Vol.223(4), pp.1276-1298
2010
DOI: https://doi.org/10.1016/j.aim.2009.09.018

Abstract

Badly approximable vectors Diophantine approximation Hausdorff dimension Schmidt's game
We show that the sets of weighted badly approximable vectors in Rn are winning sets of certain games, which are modifications of (α,β)-games introduced by W.M. Schmidt in 1966. The latter winning property is stable with respect to countable intersections, and is shown to imply full Hausdorff dimension.
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https://doi.org/10.1016/j.aim.2009.09.018View
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