ON THE MORPHOLOGY OF GAMMA-EXPANSIONS WITH DELETED DIGITS

Authors
KEANE M SMORODINSKY M SOLOMYAK B
Citation
M. Keane et al., ON THE MORPHOLOGY OF GAMMA-EXPANSIONS WITH DELETED DIGITS, Transactions of the American Mathematical Society, 347(3), 1995, pp. 955-966
Citations number
6
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
347
Issue
3
Year of publication
1995
Pages
955 - 966
Database
ISI
SICI code
0002-9947(1995)347:3<955:OTMOGW>2.0.ZU;2-X
Abstract
We investigate the size of the set of reals which can be represented i n base gamma using only the digits 0,1,3. It is shown that this set ha s Lebesgue measure zero for gamma less than or equal to 1/3 and equals an interval for gamma greater than or equal to 2/5. Our main goal is to prove that it has Lebesgue measure zero for a certain countable sub set of (1/3,2/5).