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Sums of Cantor sets

Published online by Cambridge University Press:  01 December 1997

CARLOS A. CABRELLI,
KATHRYN E. HARE and
URSULA M. MOLTER
CARLOS A. CABRELLI
Affiliation:
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Cdad.Universitaria, Pab. I, (1428) Bs.As., Argentina (e-mail: ccabrell@mate.dm.uba.ar) (e-mail: umolter@mate.dm.uba.ar)
KATHRYN E. HARE
Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada (e-mail: kehare@math.uwaterloo.ca)
URSULA M. MOLTER
Affiliation:
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Cdad.Universitaria, Pab. I, (1428) Bs.As., Argentina (e-mail: ccabrell@mate.dm.uba.ar) (e-mail: umolter@mate.dm.uba.ar)
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Abstract

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We find conditions on the ratios of dissection of a Cantor set so that thegroup it generates under addition has positive Lebesgue measure. Inparticular, we answer affirmatively a special case of a conjecture posed byJ. Palis.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 6 , December 1997, pp. 1299 - 1313
Copyright
1997 Cambridge University Press