If $E(X_{n+1}\vert \mathcal{F}_{n})\leq X_{n}+Y_{n}$ and $\sum Y_{n} < \infty$ how can I define a supermartingale?
112510
Prove a.s. convergence of $(X_n)_n$ satisfying $E(X_{n+1} \mid F_n) \leq X_n+Y_n$ for $\sum_n Y_n<\infty$
134302
Criteria for being a true martingale
80803
Conditional expectation $E[\log(1+X) \mid X>t]$
97968
Does $\big|\sum_{k=1}^na_k\big|\leq\sqrt{n}$ imply the convergence of $\sum_{1}^\infty \frac{a_k}{k}$?
11082
Borel-Cantelli Lemma "Corollary" in Royden and Fitzpatrick
24683
For i.i.d. $\{X_n\}$ proving $\frac1n\max\limits_{1\leqslant k\leqslant n}|X_k|\xrightarrow{\mathrm{a.s.}}0\Leftrightarrow E(|X_1|)<+∞$
113384
$\sum_{n\geq1} k_n x_n$ converges for every $x \in l_1$, then $\sup_{n\geq1} |k_n| < \infty$
147705
Show that $\mathbb{E}(T) = \sum\limits^\infty_{k=1}\mathbb{P}(T \geq k)$ for $T$ nonnegative integer valued and $E[T] < \infty$
11465
Expected value of $\max\{X_1,\ldots,X_n\}$ where $X_i$ are iid uniform.
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
135219
On the mean value of a multiplicative function: Prove that $\sum\limits_{n\leq x} \frac{n}{\phi(n)} =O(x) $
94662
Tower property of conditional expectation
85268
Convergence of $\sum_{n=1}^{\infty}{\sqrt[n]{n}-1 \over n}$
114443
martingale and stochastic Integral
38785
Prove previsibility and $E[X_{T \wedge n}] \le E[X_{S \wedge n}]$
95022
Help understanding proof of the following statement $E(Y) = \sum_{i = 1}^{\infty} P(Y \geq k)$
11732
Is continuous L2 bounded local martingale a true martingale?