On some generalized approximative relative derivatives (Q1088797)

The authors introduce the notion of the basic set function, which is a kind of a general outer content of a subset of the real line. Each Lebesgue-Stieltjes outer measure \(\omega^*\), induced by a strictly increasing function \(\omega\), is a basic set function. Then they define \(\omega^*\)-density of a set at a point and some generalisations of approximate limits and relative derivatives, where the approximations are in terms of \(\omega^*\)-density. Some theorems on Baire 1, Darboux and mean value properties of generalized derivatives in authors' sense are proved.