# Dimension of countable intersections of some sets arising in expansions in non-integer bases

David Färm; Tomas Persson; Jörg Schmeling

Fundamenta Mathematicae (2010)

- Volume: 209, Issue: 2, page 157-176
- ISSN: 0016-2736

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topDavid Färm, Tomas Persson, and Jörg Schmeling. "Dimension of countable intersections of some sets arising in expansions in non-integer bases." Fundamenta Mathematicae 209.2 (2010): 157-176. <http://eudml.org/doc/283185>.

@article{DavidFärm2010,

abstract = {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.},

author = {David Färm, Tomas Persson, Jörg Schmeling},

journal = {Fundamenta Mathematicae},

keywords = {beta-shift; Hausdorff dimension; non-typical points},

language = {eng},

number = {2},

pages = {157-176},

title = {Dimension of countable intersections of some sets arising in expansions in non-integer bases},

url = {http://eudml.org/doc/283185},

volume = {209},

year = {2010},

}

TY - JOUR

AU - David Färm

AU - Tomas Persson

AU - Jörg Schmeling

TI - Dimension of countable intersections of some sets arising in expansions in non-integer bases

JO - Fundamenta Mathematicae

PY - 2010

VL - 209

IS - 2

SP - 157

EP - 176

AB - 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.

LA - eng

KW - beta-shift; Hausdorff dimension; non-typical points

UR - http://eudml.org/doc/283185

ER -

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