We consider expansions of real numbers in non-integer bases. These expansions are generated by β-shifts. We prove that some sets arising in metric number theory have the countable intersection property. This allows us to consider sets of reals that have common properties in a countable number of different (non-integer) bases. Some of the results are new even for integer bases.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-2-4,
author = {David F\"arm and Tomas Persson and J\"org Schmeling},
title = {Dimension of countable intersections of some sets arising in expansions in non-integer bases},
journal = {Fundamenta Mathematicae},
volume = {209},
year = {2010},
pages = {157-176},
zbl = {1211.37047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-2-4}
}
David Färm; Tomas Persson; Jörg Schmeling. Dimension of countable intersections of some sets arising in expansions in non-integer bases. Fundamenta Mathematicae, Tome 209 (2010) pp. 157-176. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-2-4/