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Oct 26, 2018 at 13:44 comment added Nate Eldredge @RobertFurber: How about now?
Oct 26, 2018 at 13:44 history edited Nate Eldredge CC BY-SA 4.0
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Oct 26, 2018 at 7:04 comment added Robert Furber I think the first sentence still has the potential to mislead someone who doesn't already know Bochner spaces. Specifically, Bochner spaces can still be defined where $B$ is inseparable, but then part of the definition is that the range of each function lies in a separable subspace (but that subspace varies from function to function). The problem, as pointed out by Gerald Edgar, is that the OP does not add this condition.
Oct 26, 2018 at 2:30 history edited Nate Eldredge CC BY-SA 4.0
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Oct 25, 2018 at 17:29 history edited Nate Eldredge CC BY-SA 4.0
sketch proof
Oct 25, 2018 at 16:59 comment added Jochen Glueck Just to add a concrete example of quite a recent reference: see for instance "T. Hytönen, J. van Neerven, M. Veraar, L. Weis: Analysis in Banach Spaces, Volume I (2016)". Bochner spaces are treated in Chapter I in a rather general setting (for instance, without assuming $\sigma$-finiteness in general).
Oct 25, 2018 at 16:50 history answered Nate Eldredge CC BY-SA 4.0