|Title||McShane Integrability Using Variational Measure
Posted by Felipe Sumalpong, Jr.
|Authors||Sumalpong, Felipe, Jr. R. and Benitez, Julius|
|Journal||European Journal of Pure and Applied Mathematics|
|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.|