Glasnik matematički, Vol. 36 No. 1, 2001.
Original scientific paper
On functions which are almost additive modulo a subgroup
Janusz Brzdek
Abstract
Let (X,+) be a commutative semigroup, uniquely divisible by 2, (G,+) be a topological group, and K be a discrete, normal and contable subgroup of G. We show that if X is endowed with a topology and the topologies in X and G satisfy some additional conditions, then for every measurable function f mapping X into G such that f(x+y) - f(x) - f(y) ∈ K almost everywhere in X2, with respect to some ideal in X2, there is an additive function A : X → G with f(x) - A(x) ∈ K almost everywhere in X.
Keywords
Cauchy difference; measurability; additive function; σ-ideal
Hrčak ID:
4844
URI
Publication date:
1.6.2001.
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