While reading the probability space in Wikipedia, I'd found the usual formulation is a triplet, which is ${\displaystyle (\Omega ,{\mathcal {F}},P)}$.
Upon my understanding, the middle ${\mathcal {F}}$ is a power set of $\Omega$ which will be allocated with real-valued probabiilty by $P$.
If every set in this nature has power set, there might be no necessity of introduction of ${\mathcal {F}}$ I guess however, I've never thought of a set which doesn't have its power set.
Is there any set that doesn't have power set? or if not, which means every set has its power set, is there any plausible reason that ${\mathcal {F}}$ is introduced in probability formulation?