Metrics defined via discrepancy functions
In this paper the authors introduce the notion of a discrepancy function. A discrepancy function is a real extended, non-negative function \(\omega\) defined on certain pairs \((A,U)\) (where \(A\subset U\)) of subsets of a set \(X\) with the property that, for fixed \(A\), the function \(\omega\) takes arbitrarily small values as \(U\) varies. They present a number of natural examples of discrepancy functions and show how they can be used to define traditional pseudo-metrics, quasimetrics and metrics on hyperspaces of topological spaces and measure spaces.
scientific article; zbMATH DE number 5151654