Hello, Given a Brownian Motion process B(t) for 0≤t≤T, we can write it more explicitly as B(t,ω) where ω[itex]\in[/itex]Ω, where Ω is the underlying sample space. My question is: what is the cardinality of Ω. I.e. what is |Ω|? My thoughts are that it is an uncountable set, based on the observation that B(t) ~ N(0,t), and thus takes values in the real numbers. Am I correct, is this simple observation enough, or is a more rigorous proof needed?