The Wikipedia page on stochastic processes defines a stochastic process as:
A stochastic process is defined as a collection of random variables defined on a common probability space (Ω,F,P), where Ω is a sample space, F is a σ-algebra, and P is a probability measure; and the random variables, indexed by some set T, all take values in the same mathematical space S, which must be measurable with respect to some σ-algebra Σ.
Now, unfortunately, this definition confuses me more than it enlightens me. I am confused by the difference between Ω and S, and F and Σ. It seems to me that the definition of a sample space is the set of all of possible outcomes/values, so the definitions of Ω and S identical to me.
Thanks for your effort! I have already searched this website to see if the question already exists, but I could not find it.