Showing that $\mathsf{Cov}(f(X), g(Y)) \geq 0$ for non-decreasing $f$ and $g$ taking values on $\mathbb{R}$.
52129
covariance of increasing functions
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
23071
Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$
82371
$f$ is an entire function with Im $f\geq 0$
152613
Injection from $\mathbb{N}\to\{0,1\}$ to the set of all monotonic decreasing functions from $\mathbb{N}\to\mathbb{Z}$
136574
Show $g^{(n)}(0)=0$ for all $n$
62879
Question about the proof of $GCH$ holds in $\mathbf L$
119735
Show that $\mathbb{E}(g(T-p)) < \mathbb{E}(g(S-p))$ for any convex function $g$ if $T$ and $S$ are estimators of $p$
121771
Proof $f(x)\equiv 0$
67234
The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
25242
Find $\operatorname{Cov}(F_n^* (x), F_n^* (y))$ for fixed real numbers $x, y$ where $F_n^* (x)$ is a sample distribution function
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
125723
Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$
63526
Proving that $(\sup_{x\in R}|f'(x)|)^2\leq 4\sup_{x\in R}|f(x)|\cdot\sup_{x\in R}|f''(x)|$.
63410
Proof on showing if F(x,y,z)=0 then product of partial derivatives (evaluated at an assigned coordinate) is -1
98098
Show that $\mu_{F}$ is a measure on $(\mathbb{R},\mathcal{S})$.
11710
How to show that $\mathbb{Q}$ is not $G_\delta$