I'm looking for references on the topic of measurable functions on Banach spaces. Specifically, if $X$ and $Y$ are "nice" Banach spaces (separable, etc.) endowed with $\sigma$-algebras so that $(X,\Sigma)$ and $(Y, \text{T})$ are measurable spaces, what are the properties of measurable functions $f : (X,\Sigma)\to(Y,\text{T})$? I assume the scalar multiple & sum of measurable functions is itself measurable (though I haven't checked if this is true, I just assumed the proofs would be similar enough to the proofs for measurable real valued functions), but what about other properties? Things I'm interested in are:
If $f$ is measurable, and $A\in\mathcal{L}(X)$ is linear and continuous (equivalently bounded), is $f\circ A$ measurable? What if $A$ is compact?
If $f$ is measurable, is $\|f\| : (X,\Sigma)\to\mathbb{R}_{\ge 0}$ measurable (with respect to Borel sets or Lebesgue measurable sets on $\mathbb{R}$)?
If $Y$ is a Banach algebra, and $f$ and $g$ are measurable, then is $fg$ measurable?
I've found it surprisingly difficult to find resources on these topics, topics which I thought would've been pretty standard functional analysis topics. What are some good resources to learn about these things?