I'm reading a book on Lyapunov Exponents by Lian and Lu in which they refer to strong measurability of operator-valued maps. They define this by saying an operator valued map $T:\Omega\to L(X,X)$ is strongly measurable if for any fixed $x\in X$, the map $\omega\mapsto T(\omega)(x)$ is measurable (without any mention of the $\sigma$-algebra that they're referring to).

I looked on Wikipedia, but wasn't able to get much more there, nor was I able to find a solid reference. I *think* I now understand what the authors meant and have proved a few lemmas solidifying the definition etc., but I would like to be able to look at a more solid reference to avoid re-inventing the wheel if possible.

Thanks for any suggestions...