I need reference on handling uncountably infinite sample spaces in probability considerations .
To be more specific , I wish to investigate random walks with the following as a starting point : any random walk that has a specified initial path ($P$) of length $l $ is of form $\{P\} \times \Omega $ where $\Omega = \{+,-\}^\infty$ and $P \in \{+,-\}^l$ .
It would be nice if there is a reference on treatment of such uncountable sample spaces as I am uncomfortable working with such sample spaces .