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Fundam. Prikl. Mat., 2015, Volume 20, Issue 6, Pages 237–258 (Mi fpm1696)  

This article is cited in 1 scientific paper (total in 1 paper)

The Leibniz differential and the Perron–Stieltjes integral

E. V. Shchepin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We implement Leibniz's idea about the differential as the length of an infinitesimally small elementary interval (a monad) in the 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.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005


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English version:
Journal of Mathematical Sciences (New York), 2018, 233:1, 157–171

Bibliographic databases:

UDC: 517.22+517.3+517.518.12+517.518.126

Citation: E. V. Shchepin, “The Leibniz differential and the Perron–Stieltjes integral”, Fundam. Prikl. Mat., 20:6 (2015), 237–258; J. Math. Sci., 233:1 (2018), 157–171

Citation in format AMSBIB
\Bibitem{Shc15}
\by E.~V.~Shchepin
\paper The Leibniz differential and the Perron--Stieltjes integral
\jour Fundam. Prikl. Mat.
\yr 2015
\vol 20
\issue 6
\pages 237--258
\mathnet{http://mi.mathnet.ru/fpm1696}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1778991}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 233
\issue 1
\pages 157--171
\crossref{https://doi.org/10.1007/s10958-018-3932-8}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049222448}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Korneev, E. V. Shchepin, “$L_\infty $-locality of three-dimensional Peano curves”, Proc. Steklov Inst. Math., 302 (2018), 217–249  mathnet  crossref  crossref  isi  elib
  • Фундаментальная и прикладная математика
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