The Schweizer-Smítal metric (Q1851425)

Schweizer and Smítal introduced a measure of chaos generated by a continuous function. This is used in order to define two distribution functions; then the measure in question is the area between their graphs. This same measure can be used for any pair of distribution functions, thus giving rise to a new metric, called \(d_I\), on the space of distribution functions. The topology of \(d_I\) differs from that of the classical Lévy metric, but the two topologies are equivalent when one considers distribution functions with fixed compact support.