McShane Integrability Using Variational Measure

Authors

  • Felipe Raypan Sumalpong Jr Mindanao State University - Iligan Institute of Technology
  • Julius V. Benitez

DOI:

https://doi.org/10.29020/nybg.ejpam.v13i2.3659

Keywords:

McShane integral, integrable set, McShane $\delta$-variation, McShane variational measure, variation zero, Cauchy extension

Abstract

If f : [a, b] → R is McShane integrable on [a, b], then f is McShane integrable on every Lebesgue measurable subset of [a, b]. However, integrability of a real-valued function on [a, b] does not imply McShane integrability on any E ⊆ [a, b]. In this paper, we give a characterization for the McShane integrability of f : [a, b] → R over E ⊆ [a, b] using concept of variational measure.

Author Biography

Felipe Raypan Sumalpong Jr, Mindanao State University - Iligan Institute of Technology

Department of Mathematics and Statistics

Assistant Professor IV

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Published

2020-04-29

How to Cite

Sumalpong Jr, F. R., & Benitez, J. V. (2020). McShane Integrability Using Variational Measure. European Journal of Pure and Applied Mathematics, 13(2), 303–313. https://doi.org/10.29020/nybg.ejpam.v13i2.3659

Issue

Vol. 13 No. 2: (April 2020)

Section

Nonlinear Analysis

License

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European Journal of Pure and Applied Mathematics will be Copyright Holder.