The Birkhoff Weak Integral of Functions Relative to a Set Function in Banach Spaces Setting
Anca Croitoru, Alina Cristiana Gavriluţ, Alina Emilia Iosif · WSEAS Transactions on Mathematics archive · 2017
In this paper, we define and study the Birkhoff weak integral in two cases: for vector functions relative to a non-negative set function and for real functions with respect to a vector set function. Some comparison results and classical integral properties are obtained: the linearity relative to the function and the measure, and the monotonicity with respect to the function, the measure and the set