In mathematics, Bochner spaces are a generalization of the concept of spaces to functions whose values lie in a Banach space which is not necessarily the space or of real or complex numbers.
The space consists of (equivalence classes of) all Bochner measurable functions with values in the Banach space whose norm lies in the standard space. Thus, if is the set of complex numbers, it is the standard Lebesgue space.
Almost all standard results on spaces do hold on Bochner spaces too; in particular, the Bochner spaces are Banach spaces for
Bochner spaces are named for the mathematician Salomon Bochner.