## Bad(s,t) is hyperplane absolute winning

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### Publication details

Journal Acta Arithmetica Published - 2014 2 164 8 145-152 English

### Abstract

J. An (2013) proved that for any $s,t \geq 0$ such that $s + t = 1$, $\mathbf{Bad}(s,t)$ is $(34\sqrt 2)^{-1}$-winning for Schmidt's game. We show that using the main lemma from An's paper one can derive a stronger result, namely that $\mathbf{Bad}(s,t)$ is hyperplane absolute winning in the sense of Broderick, Fishman, Kleinbock, Reich, and Weiss (2012). As a consequence one can deduce the full dimension of $\mathbf{Bad}(s,t)$ intersected with certain fractals.

### Bibliographical note

This is an author produced version of a paper accepted for publication in Acta Arithmetica. Uploaded in accordance with the publisher's self-archiving policy.

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