On a composite functional equation satisfied almost everywhere.

Abstract: The purpose of the paper is to deal with functions on an Abelian group which satisfy the following composite functional equation: for almost all pairs . The concept of “almost all pairs” is defined in an abstract manner. Our main result states that, under some technical assumptions, every such a function behaves in some sense similar to a function which satisfy the above equation for all pairs . [Copyright &y& Elsevier]