Fundamentalnaya i Prikladnaya Matematika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Journal history

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Fundam. Prikl. Mat.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Fundamentalnaya i Prikladnaya Matematika, 2015, Volume 20, Issue 6, Pages 237–258 (Mi fpm1696)  
This article is cited in 1 scientific paper (total in 2 paper)

The Leibniz differential and the Perron–Stieltjes integral

E. V. Shchepin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (207 kB) Citations (2)
References:
PDF
HTML
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
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 233, Issue 1, Pages 157–171
DOI: https://doi.org/10.1007/s10958-018-3932-8
Bibliographic databases:
Document Type: Article
UDC: 517.22+517.3+517.518.12+517.518.126
Language: Russian
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://mathscinet.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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049222448}
Linking options:
  • https://www.mathnet.ru/eng/fpm1696
  • https://www.mathnet.ru/eng/fpm/v20/i6/p237
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Фундаментальная и прикладная математика
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024