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Title McShane Integrability Using Variational Measure
Posted by Felipe Sumalpong, Jr.
Authors Sumalpong, Felipe, Jr. R. and Benitez, Julius
Publication date 2020/04
Journal European Journal of Pure and Applied Mathematics
Volume 13
Issue 2
Pages 303-313
Publisher Ansari Education and Research Society
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.
Index terms / Keywords McShane integral, integrable set, McShane delta-variation, McShane variational measure, variation zero, Cauchy extension.