Advanced Search

The aim of this paper is to introduce a generalization of the classical absolute continuity to a relative case, with respect to a subset $M$ of an interval $I$. This generalization is based on adding more requirements to disjoint systems ${\left\{(a_k,b_k)\right\}}_K$ from the classical definition of absolute continuity – these systems should be not too far from $M$ and should be small relative to some covers of $M$. We discuss basic properties of relative absolutely continuous functions and compare this class with other classes of...