**A. Kharazishvili**

## On Generalized Step-Functions and Superposition
Operators

**Abstract:**

For a given $\sigma$-ideal of sets, the notion of a generalized step-function is
introduced and investigated in connection with the problem of sup-measurability
of certain functions of two variables, regarded as superposition operators.

**Keywords:**

Generalized step-function, superposition operator, Lebesgue measure, Baire
property, $\sigma$-ideal of sets, base of a $\sigma$-ideal.

**MSC 2000:** 28A05, 28D05