$\mathbf{Bad}(s,t)$ is hyperplane absolute winning
| Autor: | Nesharim, Erez, Simmons, David S. |
|---|---|
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Acta Arith. 164 (2014), no. 2, 145--152 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. |
| Databáze: | arXiv |
| Externí odkaz: |
|