A convergence theorem on the dunford integral
Solikhin Solikhin, Abdul Muhaiminul Aziz, Y.D. Sumanto, SU R Heri · Journal of Physics Conference Series · 2021
Abstract This article discusses the convergence theorem of the Dunford integrals. We examine the sufficient conditions so that limit of the sequence of integral value whose Dunford integrable is same as limit of functions sequence. We have obtained that to guarantee a function to be Dunford integrable and its limit of functions sequence are same as value of the functions, then a sequence of Dunford integrable function is uniform convergent or weakly convergent, weakly monoton, and its limit exist. Furthermore, its weakly convergent and bounded.