McShane Integrability Using Variational Measure

McShane Integrability Using Variational Measure

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 McSh...

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Veröffentlicht in:European journal of pure and applied mathematics 2020-01, Vol.13 (2), p.303-313
Hauptverfasser: Sumalpong Jr, Felipe Raypan, Benitez, Julius V.
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1307-5543
1307-5543
DOI:10.29020/nybg.ejpam.v13i2.3659