Journal
| 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. |