On the McShane Integral in Topological Vector Spaces

Abstract

In this paper, the McShane integral of a function with values in a topological vector space (TVS) is defined. Results such as uniqueness of the integral, the Cauchy criterion for integrability, integrability of a continuous function, linearity of the integral, and additive property on subintervals are presented. Moreover, this study shows that the TVS-version and the Banach-version of the McShane integral are equivalent whenever the space under consideration is Banach.