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
1991 Mathematics Subject Classification. 39B52.
Key words and phrases. Cauchy difference, measurability, additive function, σ-ideal.