I'm examining several function spaces like $L^p(X,\mu)$ where $X$ is a Banach space.
Is it possible to take $X = L^1([0,1])$ and then look at $L^p(X)$?
The problem I have is that I don't know what kind of measure $X=L^1([0,1])$ should have, and therefore I'm not sure whether $L^p(L^1([0,1]))$ makes sense.