I'm looking for references to what I believe to be "basic properties" of Bochner Space of the type $$L^p(\Omega; X),$$ where $X$ is a Banach space and $\Omega \subset \mathbb{R}^N$ is an opened and bounded subset.
What I mean by basic properties are the results about $L^p(\Omega; X)$ being Banach, reflexive, separable... All the books that I found use this results (some of then even enunciate it), but never prove.
Can somebody save me? :)