Twice Periodic Measurable Functions
Alonso, Alberto ; Rosenblueth, Javier F.
Real Anal. Exchange, Tome 25 (1999) no. 1, p. 387-388 / Harvested from Project Euclid
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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}
Publié le : 1999-05-15
Classification:  periodic measurable functions,  Lebesgue density theorem,  28A20 
@article{1231187613,
     author = {Alonso, Alberto and Rosenblueth, Javier F.},
     title = {Twice Periodic Measurable Functions},
     journal = {Real Anal. Exchange},
     volume = {25},
     number = {1},
     year = {1999},
     pages = { 387-388},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1231187613}
}

Alonso, Alberto; Rosenblueth, Javier F. Twice Periodic Measurable Functions. Real Anal. Exchange, Tome 25 (1999) no. 1, pp.  387-388. http://gdmltest.u-ga.fr/item/1231187613/