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On almost additive functions

Published online by Cambridge University Press:  17 April 2009

Janusz Brzdȩk
Janusz Brzdȩk
Affiliation:
Department of Mathematics, Pedagogical University, Rejtana 16 A, 35-310 Rzeszów, Poland
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Abstract

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Let (S, +) be a semigroup and (H, +) be a group (neither necessarily commutative). Suppose that J ⊂ 2s is a proper ideal in S such that

and Ω(J) = {M ⊂ S2 : there exists U(M)∈ J with M [x] ∈ J for x ∈ S/U(M)}, where M[x] = {y ∈ S : (y, x) ∈ M}. We show that if f : S → H is a function satisfying

then there exists exactly one additive function F : S → H with F(x) = f(x) J-almost everywhere in S.

We also prove some results concerning regularity of the function F.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 2 , October 1996 , pp. 281 - 290
Copyright
Copyright © Australian Mathematical Society 1996

References

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