MathOverflow

Starting point. Early on in the first analysis class, it is taught that any sequence $s:\mathbb{N}\to [0,1]$ has a convergent subsequence. This question is about whether every sequence has a convergent subsequences such that the index set is dense in...

Let $A$ be a finite-dimensional algebra over a field, and let $M$ be a finitely generated indecomposable $A$-module.
I will say that $M$ is Fac-prime if whenever$M \in \mathrm{Fac}\{X_1,X_2\}$, then either $M \in \mathrm{Fac} X_1$ or $M \in \mathrm{Fac} X_2$.Here, for an $A$-module $X$, the condition $M \in \mathrm{Fac} X$ means that there exists some $n \ge 1$ and...

The following problem came to mind, for which the "laundry folding problem" name seems appropriate. Suppose you have an arbitrary simple polygon which you can fold using straight folds an arbitrary number of times. The goal is to reach some (simpler...

Assume $f(t,\omega)$ is (i)separable, (ii) measurable as function from $((0,T)×\Omega)$ into $R$ and (iii) is adapted to the filtration $F_t, 0<t<T$Also $\int_0^Tf^2(s)ds<\infty$ almost sure.
Is integral $\int_0^tf(s,\omega)ds$ measurable with respect to $F_t$?...