Additive functions modulo a countable subgroup of ${\Bbb R}$

Volume 95 / 2003

Nikos Frantzikinakis 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 $G$.

Authors

  • Nikos Frantzikinakis331 McAllister Building
    State College, PA 16801, U.S.A.
    e-mail

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