  In this paper, we extend the Hake-McShane and Hake-Henstock-Kurzweil
integrals of Banach space valued functions from m-dimensional open and bounded
sets to m-dimensional sets G such that |G \ Go| = 0. We will prove the full
descriptive characterizations of new integrals in terms of the locally McShane
and locally Henstock-Kurzweil integrals.
