I am confused about the concept of powerset in the following context.
I am reading the Bandit Algorithm book (http://banditalgs.com/) by Csaba Szepesvari. There it gives the following theorem:
Theorem 2.1: Let $\Omega = [0,1]$ and $\mathcal{F}$ is the powerset of $\Omega$. Then there does not exist a measure $\mathbb{P}$ on $(\Omega, \mathcal{F})$ such that $\mathbb{P}([a,b]) = b-a$ for all $0\leq a \leq b \leq 1$.
What does the powerset of $\Omega$ look like since there are infinitely many real numbers in it?