If $X$ is independent of $Y$ and $Y$ is independent of $Z$, is $X$ independent of $Z$?
126963
Is the sum of two variables independent of a third variable, if they are so on their own?
158551
If $X \perp Y$ and $X+Y \in L^1$ then $X,Y \in L^1$
97049
If $v_1,...,v_m$ are linearly independent, then the span $v_1+w,...,v_m+w$ has dimension $\ge m-1$
127052
Independence of non-constant real variables
85076
Is it true that $d(x,Y)=d(x,y_0)$ for some $y_0 \in Y$ when $Y$ is closed?
129926
Assume $A,B,C,D$ are pairwise independent events. Decide if $A\cap B$ and $B\cap D$ are independent
20728
Proof that this is independent
145039
Algebraic independence over $\overline{\mathbb Q}$ and over $\mathbb Q$
135085
The mutual density of $X,Y$ in $\{|t|+|s|<1\}$ is constant, are $X,Y$ independent?
6291
Proving something is a linearly independent subset
155136
$x\in \{\{\{x\}\}\}$ or not?
150141
Showing $X$, $Y$ are not independent but $\operatorname{Cov}[X, Y] = 0$
39378
Moment generating functions/ Characteristic functions of $X,Y$ factor implies $X,Y$ independent.
38461
If random variables are drawn from an identical distribution, why doesn't this guarantee they are independent?
138798
Independence and conditional distribution
121853
$X$,$Y$,$Z$ mutually independent implies $X+Y$ independent of $Z$
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?