  The purpose of this article is to present the construction and basic
properties of the general Bochner integral. The approach presented here is
based on the ideas from the book The Bochner Integral by J. Mikusinski where
the integral is presented for functions defined on $\mathbb{R}^N$. In this
article we present a more general and simplified construction of the Bochner
integral on abstract measure spaces. An extension of the construction to
functions with values in a locally convex space is also considered.
