On the morphology of γ-Expansions with deleted digits

Mike Keane; Meir Smorodinsky; Boris Solomyak

doi:10.1090/S0002-9947-1995-1290723-X

On the morphology of γ-Expansions with deleted digits

Mike Keane
, Meir Smorodinsky
, Boris Solomyak

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

We investigate the size of the set of reals which can be represented in base γ using only the digits 0, 1, 3. It is shown that this set has Lebesgue measure zero for γ < 1/3 and equals an interval for γ >2/5. Our main goal is to prove that it has Lebesgue measure zero for a certain countable subset of (1/3, 2/5).

Original language	English
Pages (from-to)	955-966
Number of pages	12
Journal	Transactions of the American Mathematical Society
Volume	347
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9947-1995-1290723-X
State	Published - Mar 1995
Externally published	Yes

Keywords

Cantor sets
Hausdorff dimension
β-expansions

Access to Document

10.1090/S0002-9947-1995-1290723-X

Cite this

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abstract = "We investigate the size of the set of reals which can be represented in base γ using only the digits 0, 1, 3. It is shown that this set has Lebesgue measure zero for γ < 1/3 and equals an interval for γ >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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AB - We investigate the size of the set of reals which can be represented in base γ using only the digits 0, 1, 3. It is shown that this set has Lebesgue measure zero for γ < 1/3 and equals an interval for γ >2/5. Our main goal is to prove that it has Lebesgue measure zero for a certain countable subset of (1/3, 2/5).

KW - Cantor sets

KW - Hausdorff dimension

KW - β-expansions

UR - https://www.scopus.com/pages/publications/0000922898

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On the morphology of γ-Expansions with deleted digits

Abstract

Keywords

Access to Document

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