is saying that this set of omegas is measurable. (It's not saying that X(omega) is upper bounded by x.) This is a somewhat technical condition on random variables. If you are in a measure-theoretic probability class, it is important, but otherwise you don't need to worry about this --- the main thing to know is that a random variable is a function from Omega to R.
In the definition of a random variable, what is the purpose of x as an upper boundary to X(ω)?
alkalait 5 months ago
@alkalait The condition that
{omega : X(omega)<=x} is in A
is saying that this set of omegas is measurable. (It's not saying that X(omega) is upper bounded by x.) This is a somewhat technical condition on random variables. If you are in a measure-theoretic probability class, it is important, but otherwise you don't need to worry about this --- the main thing to know is that a random variable is a function from Omega to R.
mathematicalmonk 5 months ago