Why is the probability measure P not defined on the power set of $\Omega$, but on it's sigma algebra?
9762
Why do we need sigma-algebras to define probability spaces?
136795
A non-measurable set of given outer measure
55157
$\sigma$-algebras on a countable set is generated by partitions of the set
25811
Intuition for Conditional Expectation of $\sigma$-algebra
115860
Is a measure for a sigma algebra determined by its values for a generator of the sigma algebra?
43894
If $S$ is an infinite $\sigma$ algebra on $X$ then $S$ is not countable
53642
Cardinality of Borel sigma algebra
117185
The union of a strictly increasing sequence of $\sigma$-algebras is not a $\sigma$-algebra
35140
Existence of minimal $\sigma$-algebra and transfinite induction
102030
Getting the expectation symbol to behave like $\sum$ instead of $\Sigma$
73619
Why is $(\mathbb{R}, \mathcal{P}(\mathbb{R}))$ called a measurable space when actually is not?
157599
what is the meaning of $F_\sigma$ and $G_\delta?$
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
142594
Verifying the interpretation of stopping times and stopping time $\sigma$-algebras
134768
Borel hierarchy doesn't "collapse" before $\omega_1$
62737
Intuition behind measurable random variables and $\sigma$-algebra
55717
cardinality of the Borel $\sigma$-algebra of a second countable space