# Modified Schmidt games and Diophantine approximation with weights - Mathematics > Number Theory

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Abstract: We show that the sets of weighted badly approximable vectors in $\Bbb R^n$are winning sets of certain games, which are modifications of$\alpha,\beta$-games introduced by W. Schmidt in 1966. The latter winningproperty is stable with respect to countable intersections, and is shown toimply full Hausdorff dimension.

Autor: Dmitry Kleinbock, Barak Weiss

Fuente: https://arxiv.org/