Email this article The Leibniz Differential and the Perron–Stieltjes Integral
- Authors: Shchepin E.V.1
-
Affiliations:
- Steklov Mathematical Institute of the Russian Academy of Sciences
- Issue: Vol 233, No 1 (2018)
- Pages: 157-171
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241552
- DOI: https://doi.org/10.1007/s10958-018-3932-8
- ID: 241552
Cite item
Open Access
Access granted
Subscription Access
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.
About the authors
E. V. Shchepin
Steklov Mathematical Institute of the Russian Academy of Sciences
Author for correspondence.
Email: scepin@mi.ras.su
Russian Federation, Moscow
