On Characterizing Classes of Functions in Terms of Associated Sets

Abstract

Let κ be a class of real valued functions defined on an interval which need not be bounded. The class κ is said to be characterized in terms of associated sets if there exists a family of sets of real numbers P such that f ∈ κ if and only if for every real number α the sets a remembers of P. Many classes of functions have been characterized in terms of associated sets. The chart below summarizes a few such characterizations.