Abstract
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 $\{(a_k, b_k)\}_K$ 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 generalized absolutely continuous functions.
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