I'm studying Markov Processes in Rick Durrett - Probability: Theory and Examples and he's doing something I simply don't understand, though I reckon it's probably quite simple. Here goes (an example from introducing conditional expectations):
Given a probability space $\left(\Omega,\mathcal{F}_{0},P\right)$ a $\sigma\text{-field}\,\mathcal{F}\subset\mathcal{F}_{0}$ and a random variable $X\in\mathcal{F}_{0}$...
What does it mean for $X\in\mathcal{F}_{0}$? I mean, the image of X has to be Borel, right? It belonging to a $\sigma$-algebra in our probability space doesn't make sense to me.
Hope someone will help, Henrik
p.s. Wow the math on this site works good!