Dimension of Countable Intersections of Some Sets Arising in Expansions in Non-Integer Bases

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Sammanfattning

Abstract in Undetermined
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.
Originalspråkengelska
Sidor (från-till)157-176
TidskriftFundamenta Mathematicae
Volym209
DOI
StatusPublished - 2010

Ämnesklassifikation (UKÄ)

  • Matematik

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