Open Access
1999/2000 Twice Periodic Measurable Functions
Alberto Alonso, Javier F. Rosenblueth
Real Anal. Exchange 25(1): 387-388 (1999/2000).


In this note we prove that, for $a,b \in (0,1)$ and $f$ a measurable function mapping $[0,1]$ to $\R$, the following statements are equivalent: \begin{itemize} \item[(i)] $f(x)=f(x-a)$ a.e.~in $[a,1]$ and $f(x)=f(x-b)$ a.e.~in $[b,1]$ implies that $f$ is a.e.~constant in $[0,1]$. \item[(ii)] $a + b \le 1$ and $a/b$ is irrational. \end{itemize}


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Alberto Alonso. Javier F. Rosenblueth. "Twice Periodic Measurable Functions." Real Anal. Exchange 25 (1) 387 - 388, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 5 January 2009

zbMATH: 1015.28005
MathSciNet: MR1758895

Primary: 28A20

Keywords: Lebesgue density theorem , periodic measurable functions

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 1 • 1999/2000
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