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

Färm, David LU ; Persson, Tomas LU and Schmeling, Jörg LU (2010) In Fundamenta Mathematicae 209. p.157-176
Abstract (Swedish)
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.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
beta-shift, Hausdorff dimension, non-typical points
in
Fundamenta Mathematicae
volume
209
pages
157 - 176
publisher
Institute of Mathematics, Polish Academy of Sciences
external identifiers
  • wos:000283036500004
  • scopus:78649529286
ISSN
0016-2736
DOI
10.4064/fm209-2-4
language
English
LU publication?
yes
id
c53b7487-240a-43a0-ac89-32df885b42bb (old id 1668596)
date added to LUP
2010-09-10 14:37:48
date last changed
2018-05-29 12:29:57
@article{c53b7487-240a-43a0-ac89-32df885b42bb,
  abstract     = {<b>Abstract in Undetermined</b><br/><br>
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.},
  author       = {Färm, David and Persson, Tomas and Schmeling, Jörg},
  issn         = {0016-2736},
  keyword      = {beta-shift,Hausdorff dimension,non-typical points},
  language     = {eng},
  pages        = {157--176},
  publisher    = {Institute of Mathematics, Polish Academy of Sciences},
  series       = {Fundamenta Mathematicae},
  title        = {Dimension of Countable Intersections of Some Sets Arising in Expansions in Non-Integer Bases},
  url          = {http://dx.doi.org/10.4064/fm209-2-4},
  volume       = {209},
  year         = {2010},
}