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