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The Leibniz Differential and the Perron–Stieltjes Integral

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Abstract

We implement Leibniz’s idea about the differential as the length of an infinitesimally small elementary interval (a monad) in a form satisfying modern standards of rigor. The concept of sequential differential introduced in this paper is shown to be in good alignment with the standard convention of the integral calculus. As an application of this concept we simplify and generalize the construction of the Perron–Stieltjes integral.

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References

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Authors and Affiliations

  1. Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

    E. V. Shchepin

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  1. E. V. Shchepin
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Correspondence to E. V. Shchepin.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 20, No. 6, pp. 237–258, 2015.

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Shchepin, E.V. The Leibniz Differential and the Perron–Stieltjes Integral. J Math Sci 233, 157–171 (2018). https://doi.org/10.1007/s10958-018-3932-8

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  • DOI: https://doi.org/10.1007/s10958-018-3932-8

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