Skip to main content
SpringerLink
Log in

Several comments on the Henstock-Kurzweil and McShane integrals of vector-valued functions

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

We make some comments on the problem of how the Henstock-Kurzweil integral extends the McShane integral for vector-valued functions from the descriptive point of view.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. Deville, J. Rodríguez: Integration in Hilbert generated Banach spaces. Isr. J. Math. 177 (2010), 285–306.

    Article  MATH  Google Scholar 

  2. D. H. Fremlin: The Henstock and McShane integrals of vector-valued functions. Ill. J. Math. 38 (1994), 471–479.

    MathSciNet  MATH  Google Scholar 

  3. D. H. Fremlin: The generalized McShane integral. Ill. J. Math. 39 (1995), 39–67.

    MathSciNet  MATH  Google Scholar 

  4. D. H. Fremlin, J. Mendoza: On the integration of vector-valued functions. Ill. J. Math. 38 (1994), 127–147.

    MathSciNet  MATH  Google Scholar 

  5. R. A. Gordon: The McShane integral of Banach-valued functions. Ill. J. Math. 34 (1990), 557–567.

    MATH  Google Scholar 

  6. R. A. Gordon: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. Graduate Studies in Mathematics, Vol. 4. American Mathematical Society (AMS), Providence, 1994.

    MATH  Google Scholar 

  7. P. Hájek, V. Montesinos Santalucía, J. Vanderwerff, V. Zizler: Biorthogonal Systems in Banach Spaces. CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC. Springer, New York, 2008.

    Google Scholar 

  8. J. Kurzweil, Š. Schwabik: On McShane integrability of Banach space-valued functions. Real Anal. Exch. 29 (2003-04), 763–780.

    MathSciNet  Google Scholar 

  9. T.-Y. Lee: Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion. Math. Bohem. 130 (2005), 349–354.

    MathSciNet  MATH  Google Scholar 

  10. T.-Y. Lee, T.-S. Chew, P.-Y. Lee: On Henstock integrability in Euclidean spaces. Real Anal. Exch. 22 (1996), 382–389.

    MathSciNet  MATH  Google Scholar 

  11. J. Lindenstrauss, L. Tzafriri: Classical Banach Spaces, I. Sequence Spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 92. Springer, Berlin-Heidelberg-New York, 1977.

    MATH  Google Scholar 

  12. T.P. Lukashenko, V.A. Skvortsov, A. P. Solodov: Generalized Integrals. URSS, Moscow, 2010. (In Russian.)

    Google Scholar 

  13. K. Naralenkov: On Denjoy type extensions of the Pettis integral. Czech. Math. J. 60 (2010), 737–750.

    Article  MathSciNet  MATH  Google Scholar 

  14. S. Saks: Theory of the Integral. Dover Publications, Mineola, 1964.

    MATH  Google Scholar 

  15. C. Swartz: Norm convergence and uniform integrability for the Henstock-Kurzweil integral. Real Anal. Exch. 24 (1998), 423–426.

    MathSciNet  MATH  Google Scholar 

  16. M. Talagrand: Pettis Integral and Measure Theory. Mem. Am. Math. Soc. 307 (1984)

  17. G.-J. Ye, T.-Q. An: Remarks on Henstock integrability. Adv. Math. (China) 34 (2005), 741–745.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Methods and Information Technologies, Moscow State Institute of International Relations, Vernadskogo Ave. 76, 119454, Moscow, Russian Federation

    Kirill Naralenkov

Authors
  1. Kirill Naralenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kirill Naralenkov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Naralenkov, K. Several comments on the Henstock-Kurzweil and McShane integrals of vector-valued functions. Czech Math J 61, 1091–1106 (2011). https://doi.org/10.1007/s10587-011-0050-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10587-011-0050-x

Keywords

MSC 2010

Search

Navigation