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1995/1996 The nonconvergence of a class of measurable functions
Kali P. Rath
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Real Anal. Exchange 21(1): 304-307 (1995/1996).


Let \(\{\epsilon_n\}\) be a sequence of positive numbers converging to \(0\). For each \(n\) divide the unit interval \([0, 1]\) into sub-intervals of the type \([k \epsilon_n, (k+1) \epsilon_n)\), \(k = 0, 1, 2, \dots\) and define a function \(f^n\) as \(1, -1, 1, -1, \dots\) successively on these intervals. If \(\{f^{n_k}\}\) is any subsequence of \(\{f^n\}\) then the set of points at which \(\{f^{n_k}\}\) converges has Lebesgue measure zero. This is a generalization of the well known analogous result for Rademacher functions.


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Kali P. Rath. "The nonconvergence of a class of measurable functions." Real Anal. Exchange 21 (1) 304 - 307, 1995/1996.


Published: 1995/1996
First available in Project Euclid: 3 July 2012

zbMATH: 0846.28003
MathSciNet: MR1377540

Primary: 28A20
Secondary: 26A39

Keywords: Lebesgue measure , Rademacher functions

Rights: Copyright © 1995 Michigan State University Press

Vol.21 • No. 1 • 1995/1996
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