A. Kharazishvili

On Generalized Step-Functions and Superposition Operators

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.

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

MSC 2000: 28A05, 28D05