Abstract
This chapter discusses a general Radon–Nikodym theorem. It also presents the structure of indefinite integrals of Dobrakov integrable functions with respect to an operator-valued measure that is countably additive in the strong operator topology. These operator-valued measures include many of the interesting norm finitely-additive measures as they include the representing measures of locally compact operators C0(T, X) to Y, T locally compact, X, Y Banach spaces. A set property P is said to be a local property in a positive measure space (Τ, Σ, v) if for every E ∈ Σ, v(E) > 0, there exists F ⊂ E, v(F) > 0, such that F has property P.
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