Definition: smallest $\sigma$-algebra containing a random variable
68512
$\sigma$ algebra of collection of random variables
147486
Cartesian product of two $\sigma$-algebras is generally not a $\sigma$-algebra?
94662
Tower property of conditional expectation
78754
Showing that $E[X|X<x]$ is smaller or equal than $E[X]$ for all x
146951
Every countably generated sigma algebra is generated by a random variable
51134
If $E \in \sigma(\mathcal{C})$ then there exists a countable subset $\mathcal{C}_0 \subseteq \mathcal{C}$ with $E \in \sigma(\mathcal{C}_0)$
25811
Intuition for Conditional Expectation of $\sigma$-algebra
73869
$\mathcal{C}_1 \subseteq \mathcal{C}_2 \implies \sigma( \mathcal{C}_1) \subseteq \sigma( \mathcal{C}_2) $
70734
Entropy and the principle of least action
94980
Measurable functions in a countable co-countable $\sigma$-algebra
16048
Approximating a $\sigma$-algebra by a generating algebra
49877
Expected value and indicator random variable
138419
Sigma algebra and algebra difference
14861
If $\sigma\in S_n$ is of length $n$, then $\sigma$ generates its centralizer
104847
Minimum covariance of 2 random variables given the covariance of each with a third random variable
15872
How to prove a random variable taking values in $[0,1]$ range has variance no larger than $\frac{1}{4}$?
6190
Maximum/minimum of two random variables is a random variable