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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the morphology of $ \gamma$-expansions with deleted digits


Authors: Mike Keane, Meir Smorodinsky and Boris Solomyak
Journal: Trans. Amer. Math. Soc. 347 (1995), 955-966
MSC: Primary 11K55; Secondary 28A12
DOI: https://doi.org/10.1090/S0002-9947-1995-1290723-X
MathSciNet review: 1290723
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Abstract: We investigate the size of the set of reals which can be represented in base $ \gamma $ using only the digits $ 0,1,3$. It is shown that this set has Lebesgue measure zero for $ \gamma \leqslant 1/3$ and equals an interval for $ \gamma \geqslant 2/5$. Our main goal is to prove that it has Lebesgue measure zero for a certain countable subset of $ (1/3,2/5)$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1290723-X
Keywords: $ \beta $-expansions, Cantor sets, Hausdorff dimension
Article copyright: © Copyright 1995 American Mathematical Society