J. An proved that for any s,t ≥ 0 such that s + t = 1, Bad (s,t) is (34√2)¯¹-winning for Schmidt's game. We show that using the main lemma from [An] one can derive a stronger result, namely that Bad (s,t) is hyperplane absolute winning in the sense of [BFKRW]. As a consequence, one can deduce the full Hausdorff dimension of Bad (s,t) intersected with certain fractals.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-4,
author = {Erez Nesharim and David Simmons},
title = {Bad(s,t) is hyperplane absolute winning},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {145-152},
zbl = {1315.11057},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-4}
}
Erez Nesharim; David Simmons. Bad(s,t) is hyperplane absolute winning. Acta Arithmetica, Tome 166 (2014) pp. 145-152. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-2-4/