The Leibniz Differential and the Perron–Stieltjes Integral

The Leibniz Differential and the Perron–Stieltjes Integral

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...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) Vol. 233; no. 1; pp. 157 - 171
Main Author: Shchepin, E. V.
Format: Journal Article
Language:English
Published: New York Springer US 04-08-2018
Springer
Springer Nature B.V
Subjects:
AGREEMENTS
ALIGNMENT
Calculus
INTEGRAL CALCULUS
INTEGRALS
LENGTH
MATHEMATICAL METHODS AND COMPUTING
Mathematics
Mathematics and Statistics
Numerical analysis
Stieltjes integral
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-018-3932-8