If we have that $\tau \leq \nu$ are stopping times and that $X_n$ is a submartingale, how to show $E(X_{\tau \wedge n}) \leq E(X_{\nu \wedge n})$
38785
Prove previsibility and $E[X_{T \wedge n}] \le E[X_{S \wedge n}]$
60080
$E[e_te_s\Delta B_t\Delta B_s]$ for $\Delta B_t$ Brownian motion increments and $e_t(\omega)$ a measurable function.
3720
Supermartingale with constant Expectation is a martingale
86635
Optimizing $(X_{n}+c)^{2}$ to show that $P(\overline{X}_{n}\geq \lambda) \leq E(X_{n}^{2})/(EX_{n}^{2}+ \lambda^{2})$
50089
characterization of the existence of higher order expectation.
102042
If $X_n \stackrel{d}{\to} X$ and $c_n \to c$, then $c_n \cdot X_n \stackrel{d}{\to} c \cdot X$
105145
Show that $\mathbb{E}\left(\bar{X}_{n}\mid X_{(1)},X_{(n)}\right) = \frac{X_{(1)}+X_{(n)}}{2}$
147705
Show that $\mathbb{E}(T) = \sum\limits^\infty_{k=1}\mathbb{P}(T \geq k)$ for $T$ nonnegative integer valued and $E[T] < \infty$
8916
Is the distribution of an Ito diffusion at time t absolutely continuous wrt Lebesgue measure?
118091
Taylor expansion of $\exp(-x)$: proof tail is positive
113778
Show that $E=\{(x,\alpha)\mid 0\leq \alpha<|f(x)|\}$ is measurable if $f$ is measurable.
156901
Showing that $X\sim E[X\mid\mathcal{G}]$ implies $X=E[X\mid\mathcal{G}]$ almost surely
35911
Submartingale convergence (Durrett 5.3.1)
80350
$\limsup \frac{a_n}{b_n}0$ s.t $a_n\le Mb_n$
83476
Convergence of exponential Brownian martingale to zero almost surely
13561
Show: $E(|X|)\leqslant\liminf_{n\to\infty} E(|X_n|)$
20075
Probabilistic method Kraft-McMillan inequality