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Absolute continuity with respect to a subset of an interval

Lucie Loukotová (2017)

Commentationes Mathematicae Universitatis Carolinae

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...

Riemann-type definition of the improper integrals

Donatella Bongiorno (2004)

Czechoslovak Mathematical Journal

Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane’s definition of the Lebesgue integral by imposing a Kurzweil-Henstock’s condition on McShane’s partitions.

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