30 | 05 | 2024


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Article 50

Set-functions and some generalizations of the integrals of Foran, Iseki and Sarkhel


Mathematical reviews subject classification: 26A39, 26A45, 26A46.



There have been many attempts to unify and generalize the various known nonabsolutely convergent integrals on the real line.

To the same end, using C. M. Lee's set-functions λα we shall introduce in this paper a variety of set-functions (that extend the ordinary variation and the variations of Foran, Sarkhel, Kar, Iseki), and we shall use them to define classes of functions so that each of them can be taken as the class of primitives for an integration.

Thus, we obtain and generalize many of the known nonabsolutely convergent integrals.

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