Modified Schmidt games and Diophantine approximation with weights

Dmitry Kleinbock, Barak Weiss

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1276-1298
Number of pages23
JournalAdvances in Mathematics
Issue number4
StatePublished - 1 Mar 2010
Externally publishedYes


  • Badly approximable vectors
  • Diophantine approximation
  • Hausdorff dimension
  • Schmidt's game


Dive into the research topics of 'Modified Schmidt games and Diophantine approximation with weights'. Together they form a unique fingerprint.

Cite this