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On normal numbers for continued fractions

Published online by Cambridge University Press:  10 November 2000

COR KRAAIKAMP  and
HITOSHI NAKADA
COR KRAAIKAMP
Affiliation:
Technische Universiteit Delft and Thomas Stieltjes Institute for Mathematics, ITS (SSOR), Mekelweg 4, 2628 CD Delft, the Netherlands (e-mail: c.kraaikamp@its.tudelft.nl)
HITOSHI NAKADA
Affiliation:
Department of Mathematics, Keio University, Yokohama, 223-8522 Japan (e-mail: nakada@math.keio.ac.jp)
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Abstract

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In this paper we will show that any number normal with respect to the regular continued fraction (RCF) is also normal with respect to the continued fraction from below (BCF) and the nearest integer continued fraction (NICF). Furthermore, we will show that in case of the NICF a number is normal with respect to the RCF-expansion if and only if it is NICF-normal. This can be generalized to a larger class of semi-regular continued fraction expansions.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 5 , October 2000 , pp. 1405 - 1421
Copyright
© 2000 Cambridge University Press