A simple notation question, what is the precise definition of the space $\mathcal M (\mathcal C [0, T], E)$ ($\mathcal M^p (\mathcal C [0, T], E)$) in the context of stochastic processes where $E$ is a banach space ($\mathbb R ^d$ or $\mathbb L^p_{\lambda}(\Gamma)$ for example)?
In the article I read, this notation is introduced without definitions, seeming so to be pretty standard. In addition what is the mean of $\mathcal M (\mathcal C( [0, T], E))$ and what is the difference between the previous space?
Thanks in advance