The Leibniz Differential and the Perron–Stieltjes Integral
Journal Article
·
· Journal of Mathematical Sciences
- Steklov Mathematical Institute of the Russian Academy of Sciences (Russian Federation)
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.
- OSTI ID:
- 22773908
- Journal Information:
- Journal of Mathematical Sciences, Vol. 233, Issue 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 1072-3374
- Country of Publication:
- United States
- Language:
- English
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