Geodesic
Dimension of countable intersections of some sets arising in expansions in non-integer bases
David Färm 1   ; Tomas Persson 2   ; Jörg Schmeling 3
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland and Centre for Mathematical Sciences Lund University Box 118 SE-22100 Lund, Sweden
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
3 Centre for Mathematical Sciences Lund University Box 118 SE-22100 Lund, Sweden
Fundamenta Mathematicae, Tome 209 (2010) no. 2, pp. 157-176 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We consider expansions of real numbers in non-integer bases. These expansions are generated by $\beta $-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.
DOI : 10.4064/fm209-2-4
Keywords: consider expansions real numbers non integer bases these expansions generated beta shifts prove sets arising metric number theory have countable intersection property allows consider sets reals have common properties countable number different non integer bases results even integer bases

David Färm  1   ; Tomas Persson  2   ; Jörg Schmeling  3

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland and Centre for Mathematical Sciences Lund University Box 118 SE-22100 Lund, Sweden
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-956 Warszawa, Poland
3 Centre for Mathematical Sciences Lund University Box 118 SE-22100 Lund, Sweden 
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     title = {Dimension of countable intersections of some sets arising
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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) no. 2, pp. 157-176. doi: 10.4064/fm209-2-4

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