Additive functions modulo a countable subgroup of ${\Bbb R}$
Volume 95 / 2003
Colloquium Mathematicum 95 (2003), 117-122
MSC: Primary 39B22.
DOI: 10.4064/cm95-1-9
Abstract
We solve the mod $G$ Cauchy functional equation $$ f(x+y)=f(x)+f(y)\pmod G, $$ where $G$ is a countable subgroup of ${\mathbb R}$ and $f:{\mathbb R}\to {\mathbb R}$ is Borel measurable. We show that the only solutions are functions linear mod $G$.
