ABSTRACT
In this chapter (Ω, S, μ) will be a σ finite measure space and X will be a Banach space which contains the values of either a function or a measure. The Banach space will be either a real or a complex Banach space but the field of scalars does not matter and so we will denote it by F with the understanding that F = ℂ unless otherwise stated. We note that the theory presented here includes the case where X = ℝ n or ℂ n but it does not include all of Chapter 7 as a special case because it omits spaces such as [0, ∞]. To begin with we give the following definition.
