Kluvánek-Lewis-Henstock integral in a Banach space

Abstract

We investigate some properties and convergence theorem of Kluvánek-Lewis-Henstock µ−integrability for µ−measurable functions that we introduced in [4]. We give a µ−a.e. convergence version of Dominated (resp. Bounded) Convergence Theorem for µ. We introduce Kluvánek-Lewis-Henstock integrable of scalar-valued functions with respect to a set valued measure in a Banach space. Finally we introduce (KL)−type Dominated Convergence Theorem for the set-valued Kluvánek-Lewis-Henstock integral.