| Title |
McShane Integrability Using Variational Measure |
|
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. |
Mindanao State
University - Iligan Institute of Technology