SOLUTIONS OF A GOLAB-SCHINZEL-TYPE FUNCTIONAL EQUATION BOUNDED ON 'BIG' SETS IN AN ABSTRACT SENSE

摘要

It is well known that an exponential real function, which is Lebesgue measurable (Baire measurable, respectively) or bounded on a set of positive Lebesgue measure (of the second category with the Baire property, respectively), is continuous. Here we consider bounded on 'big' set solutions of an equation generalizing the exponential equation as well as the Golab-Schinzel equation. Moreover, we unify results into a more general and abstract case.