A book on Banach space valued random variable. I have recently become interested in probability theory that take place on a Banach space setting. What are some good books for a beginner like me?
The topic that I am especially interested in is Banach space valued $L^p(\Omega;X)$, i.e. the space of all measurable functions $f:\Omega\to X$, where $\Omega$ is a probability space and $X$ a Banach space, such that $\int||f(\omega)||_X^p\ \text{d}\omega < \infty$.

I suggest Martingales in Banach spaces by Gilles Pisier. A very preliminary version of the book (242 pages vs 580 in final version) is available on the author's website. 
The book begins with an introduction to Banach-space-valued $L^p$ spaces (i.e., Lebesgue-Bochner spaces). It's not long but clearly written and hits important points like the structure of the dual of $L^p(\Omega;X)$ with and without the Radon-Nikodým property.
