 Bochner space

In mathematics, Bochner spaces are a generalization of the concept of "Lp" spaces to functions whose values lie in a Banach space which is not necessarily the space R or C of real or complex numbers.The space "Lp(X)" consists of (equivalence classes of) all Bochner measurable functions "f" with values in the Banach space "X" whose norm "||f||X" lies in the standard "Lp" space.Thus, if "X" is the set of complex numbers, it is the standard Lebesgue "Lp" space.