@article{fcb00bcbe05c476a85b461bf4c3d7655,
title = "Modified Schmidt games and Diophantine approximation with weights",
abstract = "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.",
keywords = "Badly approximable vectors, Diophantine approximation, Hausdorff dimension, Schmidt's game",
author = "Dmitry Kleinbock and Barak Weiss",
note = "Funding Information: The authors are grateful to the hospitality of Tata Institute of Fundamental Research (Mumbai) where they had several conversations which eventually led to results described in this paper. Thanks are also due to Elon Lindenstrauss for motivating discussions, to the referee for useful comments, and to Max Planck Institute for Mathematics (Bonn) where the paper was completed. This work was supported by BSF grant 2000247, ISF grant 584/04, and NSF grants DMS-0239463, DMS-0801064.",
year = "2010",
month = mar,
day = "1",
doi = "10.1016/j.aim.2009.09.018",
language = "English",
volume = "223",
pages = "1276--1298",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press Inc.",
number = "4",
}