Additive functions modulo a countable subgroup of ℝ

Nikos Frantzikinakis. "Additive functions modulo a countable subgroup of ℝ." Colloquium Mathematicae 95.1 (2003): 117-122. <http://eudml.org/doc/285346>.

@article{NikosFrantzikinakis2003,
abstract = { We solve the mod G Cauchy functional equation f(x+y) = f(x) + f(y) (mod G), where G is a countable subgroup of ℝ and f:ℝ → ℝ is Borel measurable. We show that the only solutions are functions linear mod G. },
author = {Nikos Frantzikinakis},
journal = {Colloquium Mathematicae},
keywords = {functional equation modulo a countable real group; extension; Lebesgue-measurable; Borel-measurable solution; ergodic theory},
language = {eng},
number = {1},
pages = {117-122},
title = {Additive functions modulo a countable subgroup of ℝ},
url = {http://eudml.org/doc/285346},
volume = {95},
year = {2003},
}

TY - JOUR
AU - Nikos Frantzikinakis
TI - Additive functions modulo a countable subgroup of ℝ
JO - Colloquium Mathematicae
PY - 2003
VL - 95
IS - 1
SP - 117
EP - 122
AB - We solve the mod G Cauchy functional equation f(x+y) = f(x) + f(y) (mod G), where G is a countable subgroup of ℝ and f:ℝ → ℝ is Borel measurable. We show that the only solutions are functions linear mod G.
LA - eng
KW - functional equation modulo a countable real group; extension; Lebesgue-measurable; Borel-measurable solution; ergodic theory
UR - http://eudml.org/doc/285346
ER -