Semigroups of density-continuous functions (Q1823330)

The author considers four semigroups consisting of real functions of a real variable (with respect to superpositions): differentiable density continuous functions, approximately differentiable density continuous functions, a.e. approximately differentiable density continuous functions and density continuous functions. He shows that these semigroups (in the above order) form a strictly increasing sequence and that all semigroups have the inner automorphism property. This paper is a continuation of earlier papers by the same author.