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

35 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

@article{9d72fbf0dde34e9b9f803b40e678f095,

title = "On the morphology of γ-Expansions with deleted digits",

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).",

keywords = "Cantor sets, Hausdorff dimension, β-expansions",

author = "Mike Keane and Meir Smorodinsky and Boris Solomyak",

year = "1995",

month = mar,

doi = "10.1090/S0002-9947-1995-1290723-X",

language = "אנגלית",

volume = "347",

pages = "955--966",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "3",

}

TY - JOUR

T1 - On the morphology of γ-Expansions with deleted digits

AU - Keane, Mike

AU - Smorodinsky, Meir

AU - Solomyak, Boris

PY - 1995/3

Y1 - 1995/3

N2 - 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).

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 - http://www.scopus.com/inward/record.url?scp=0000922898&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1995-1290723-X

DO - 10.1090/S0002-9947-1995-1290723-X

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0000922898

SN - 0002-9947

VL - 347

SP - 955

EP - 966

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 3

ER -

On the morphology of γ-Expansions with deleted digits

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this