The \(ap\)-McShane integral of vector valued functions and the \(ap\)-PoU-integral. (English) Zbl 1538.26021
Summary: We introduce \(ap\)-McShane integral of vector valued functions which is a generalization of McShane integral of vector valued functions, and investigate some of its properties, also we characterize \(ap\)-McShane integral of vector valued functions by the notion of equi-integrability. Finally, we find the equivalence between the \(ap\)-McShane integral by means of partitions of the unity, and the \(ap\)-PoU-integral.
MSC:
| 26A42 | Integrals of Riemann, Stieltjes and Lebesgue type |
| 26A39 | Denjoy and Perron integrals, other special integrals |
| 28B05 | Vector-valued set functions, measures and integrals |
| 26E20 | Calculus of functions taking values in infinite-dimensional spaces |
| 46G10 | Vector-valued measures and integration |
