Skip to main content

Superinfinitesimals and the calculus of the generalized riemann integral

  • Conference paper
  • First Online:
Models and Sets

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1103))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. Benninghofen: Infinitesimalien und Superinfinitesimalien, Dissertation (1982) RWTH Aachen

    Google Scholar 

  2. B. Benninghofen, M. M. Richter: General Theory of Superinfinitesimals (1983), preprint.

    Google Scholar 

  3. J. Dieudonné: Grundzüge der modernen Analysis 1, 2; Vieweg (1975).

    Google Scholar 

  4. Floret: Maß-und Integrationstheorié; Teubner (1981).

    Google Scholar 

  5. R. Henstock: Definitions of Riemann type of the variational integrals; Proc. London Math. Soc. (3), 11(1961), 402–418

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Henstock: A Riemann type integral of Lebesque power, Canad. J. Math. 20(1968), 79–87.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Henstock: The equivalence of generalized forms of the Ward, variational, Denjoy Stieltjes and Penon — Stieltjes integrals; Proc. London Math. Soc. 10(1960), 281–303.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter; Czechoslovak. Math. J. 7(82) (1957) 418–446

    MathSciNet  MATH  Google Scholar 

  9. J. Kurzweil: Nicht absolut konvergente Integrale; Teubner — Texte zur Mathematik, Band 26 (1980).

    Google Scholar 

  10. R. M. McLeod: The generalized Riemann integral; The Carus Mathematical Monographs (1980).

    Google Scholar 

  11. E. J. McShane: A unified theory of integration; Amer. Math. Monthly, 80(1973) 349–359.

    Article  MathSciNet  MATH  Google Scholar 

  12. I. P. Natanson: Theory of the functions of a real variable.

    Google Scholar 

  13. E. Nelson: Internal Set Theory; Bull. Amer. Math. Soc. 83, 1165–1198.

    Google Scholar 

  14. M. M. Richter: Ideale Punkte, Monaden und Nichtstandardmethoden; Vieweg 1982

    Google Scholar 

  15. W. Rudin: Real and Complex Analysis; Mc Graw — Hill Series in Higher Mathematics

    Google Scholar 

  16. S. Saks: Theory of the Integral; Monografie Matematyczne VIII, 1937.

    Google Scholar 

  17. K. D. Stroyan, J.M. Bayod: Foundations of infinitesimal stochastic Analysis, to appear.

    Google Scholar 

  18. K. D. Stroyan, W. A. J. Luxemburg: Introduction to the Theory of Infinitesimals; Academic Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Gert H. Müller Michael M. Richter

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Benninghofen, B. (1984). Superinfinitesimals and the calculus of the generalized riemann integral. In: Müller, G.H., Richter, M.M. (eds) Models and Sets. Lecture Notes in Mathematics, vol 1103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099379

Download citation

  • DOI: https://doi.org/10.1007/BFb0099379

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13900-3

  • Online ISBN: 978-3-540-39115-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics