I am not that familiar in proving measurability of a function. The definition I know is that the preimage of measurable sets has to be measurable again. But how to prove that seems difficult to me at the first glance. I do have the following exercise: Let be a Brownian motion on with continuous trajectories/paths. Consider the product space
where is the Lebesgue measure. Show that the mapping () defined from that space to is measurable. How can I prove this? I think the continuity is important, but I dont know how to involve it. Any help is appreciated.