Is $\ln\{E[f(x)]\}$ equal to $E\{\ln[f(x)]\}$?
107058
Prove that $E(X\ln X)\le E X E\ln X$
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
35454
Is it correct to write $\Bbb E[X]$ or $\Bbb E_{\theta}[X]$?
93806
$\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
79011
If $(F:E)<\infty$, is it always true that $\operatorname{Aut}(F/E)\leq(F:E)?$
107795
If $\,f''(x) \ge f(x)$, for all $x\in[0,\infty),$ and $\,f(0)=f'(0)=1$, then is $\,f(x)>0$?
44060
If $\lim_{x \to +\infty} f'(x) = L$, then $\lim_{x \to \infty} \frac {f(x)}{x} = L$
127538
Show $f(x)=x\ln x$ is not uniformly continuous
21954
A question about $f(x)\equiv 0$
91680
Does $\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x)\,dx\,$?
57938
When do two functions become equal?
134696
How can I show that the conditional expectation $E(X\mid X)=X$?
72506
An example s.t. $E(E(X|\mathcal F_1)|\mathcal F_2)\neq E(E(X|\mathcal F_2)|\mathcal F_1)$
109109
Show that $E(XE[X|G])=E[(E[X|G)^2]$
23946
Prove the definitions of $e$ to be equivalent
15809
The problem of x = ln(x)
68241
Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$