A decomposition theorem for numbers in which the summands have prescribed normality properties
type: Item
instance of: scholarly article
title: A decomposition theorem for numbers in which the summands have prescribed normality properties
zbMATH Open document ID: 0599.10046
DOI: 10.1016/0022-314X(86)90034-X
author: Gavin Brown
author: W. Moran
author: Charles E. M. Pearce
published in: Journal of Number Theory
publication date: 1986-01-01T00:00:00Z
review text: The paper generalizes and refines previous work of the authors [J. Lond. Math. Soc., II. Ser. 32, 12--18 (1985; Zbl 0574.10051)]. Typical results may be described as follows: let \(A, B\) be multiplicatively independent subsets of \(\mathbb Z\setminus \{1\}\). There is a set \(M(w)\) which has full measure with respect to a Riesz product measure \(dq(w)\) such hat every \(x\in M(w)\) is normal to every base of \(A\) but is non-normal to every base of \(B\). Almost every real number can be expressed as a sum \(y=x_1+x_5\), \(x_1\in M(1)\), \(x_5\in M(5)\).
reviewed by: Fritz Schweiger
Mathematics Subject Classification ID: 11K16
Mathematics Subject Classification ID: 42A55
zbMATH DE Number: 3966214
zbMATH Keywords: normal numbers
zbMATH Keywords: multiplicatively independent subsets
zbMATH Keywords: Riesz product measure
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3966214