We prove that for any pair of nonnegative numbers with , the set of -dimensional -badly approximable vectors is winning for Schmidt’s game. As a consequence, we give a direct proof of Schmidt’s conjecture using his game.
"-dimensional badly approximable vectors and Schmidt’s game." Duke Math. J. 165 (2) 267 - 284, 1 February 2016. https://doi.org/10.1215/00127094-3165862