chapter  20
Generalized step-functions and superposition operators
ByGilbert W. Bassett Jr., Roger Koenker
Pages 16

The previous chapter was devoted to some properties of sup-measurable and weakly sup-measurable functions of two variables. In this chapter, for a given σ $\sigma$ -ideal of sets, we introduce the notion of a real-valued generalized step-function and investigate generalized step-functions in connection with the problem of sup-measurability of certain functions of two variables, regarded as superposition operators.