Geodesic
Additive functions modulo a countable subgroup of ${\Bbb R}$
Nikos Frantzikinakis 1
1 331 McAllister Building State College, PA 16801, U.S.A.
Colloquium Mathematicum, Tome 95 (2003) no. 1, pp. 117-122 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $G$.
DOI : 10.4064/cm95-1-9
Keywords: solve mod cauchy functional equation pmod where countable subgroup mathbb mathbb mathbb borel measurable only solutions functions linear mod

Nikos Frantzikinakis  1

1 331 McAllister Building State College, PA 16801, U.S.A. 
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 modulo a countable subgroup of ${\Bbb R}$},
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 modulo a countable subgroup of ${\Bbb R}$
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 modulo a countable subgroup of ${\Bbb R}$
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Nikos Frantzikinakis. Additive functions
 modulo a countable subgroup of ${\Bbb R}$. Colloquium Mathematicum, Tome 95 (2003) no. 1, pp. 117-122. doi: 10.4064/cm95-1-9

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