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Title: The Leibniz Differential and the Perron–Stieltjes Integral

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.

Authors:
 [1]
  1. Steklov Mathematical Institute of the Russian Academy of Sciences (Russian Federation)
Publication Date:
OSTI Identifier:
22773908
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 233; Journal 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); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; AGREEMENTS; ALIGNMENT; INTEGRAL CALCULUS; INTEGRALS; LENGTH

Citation Formats

Shchepin, E. V., E-mail: scepin@mi.ras.su. The Leibniz Differential and the Perron–Stieltjes Integral. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3932-8.
Shchepin, E. V., E-mail: scepin@mi.ras.su. The Leibniz Differential and the Perron–Stieltjes Integral. United States. doi:10.1007/S10958-018-3932-8.
Shchepin, E. V., E-mail: scepin@mi.ras.su. Wed . "The Leibniz Differential and the Perron–Stieltjes Integral". United States. doi:10.1007/S10958-018-3932-8.
@article{osti_22773908,
title = {The Leibniz Differential and the Perron–Stieltjes Integral},
author = {Shchepin, E. V., E-mail: scepin@mi.ras.su},
abstractNote = {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.},
doi = {10.1007/S10958-018-3932-8},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 1,
volume = 233,
place = {United States},
year = {2018},
month = {8}
}