Skip to main content
SpringerLink
Log in

Selection theorems, based on generalized variation and oscillation

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

In this paper we prove selection theorems for everywhere and almost everywhere convergent subsequences, based on the notion of uniformly limited oscillation, ofA, Λ-oscillation and ofA, Λ-variation, whereA is a system of intervals and Λ a sequence of reals. By this, we generalize and strengthen the selection theorems of Schrader (for oscillation) and of Waterman (for Λ-variation).

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. Bongiorno B., and Vetro P.,Su un teorema di F. Riesz, Atti Acc. Sc. Lett. Arti Palermo, serie IV,37(1977–78), parte I, 3–13.

    MathSciNet  Google Scholar 

  2. Di Piazza L., and Maniscalco C.,On generalized bounded variation, Contemporary Mathematics, A.M.S.42 (1985), 179–185.

    Google Scholar 

  3. Hardy G.H., Littlewood J.E., and Polya G.,Inequalities, 2nd ed., Cambridge University Press 1964.

  4. Perlman S.,Functions of generalized variation, Fund. Math., CV (1980), 199–211.

    MathSciNet  Google Scholar 

  5. Ramsey F.,On a problem of formal logic, Proc. London Math. Soc., (2)30 (1930), 264–286.

    Article  Google Scholar 

  6. Schrader K.,A generalization of the Helly Selection theorem, Bull. Am. Math. Soc.78 (1972), 415–419.

    Article  MATH  MathSciNet  Google Scholar 

  7. Schramm M.,Functions of Φ-bounded variation and Riemann-Stieltjes integration, Trans. Amer. Math. Soc.287 (1985), 49–63.

    Article  MATH  MathSciNet  Google Scholar 

  8. Waterman D.,On convergence of Fourier series of functions of generalized bounded variation, Studia Math.44 (1972), 107–117.

    MATH  MathSciNet  Google Scholar 

  9. Waterman D.,On Λ-bounded variation, Studia Math.57 (1976), 33–45.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica ed Applicazioni, Via Archirafi, 34, 90123, Palermo, (Italia)

    L. Di Piazza & C. Maniscalco

Authors
  1. L. Di Piazza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Maniscalco
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was partially supported by the Ministero della Pubblica Istruzione (Italy).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Di Piazza, L., Maniscalco, C. Selection theorems, based on generalized variation and oscillation. Rend. Circ. Mat. Palermo 35, 386–396 (1986). https://doi.org/10.1007/BF02843906

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02843906

Keywords

Search

Navigation