All questions with tag [math: almost-everywhere]


When $X_s<Y_t$ almost surely, for every $s<t$, implies that $X_s<Y_t$ for every $s<t$, almost surely?

When I have shown, for $s\le t$ and for two continuous stochastic process an inequality: $$ X_s \le Y_t$$ P-a.s. How can I deduce that this P-a.s. simultaneously for all rational $s\le t$ ? Thank you for your help EDIT: According to Ilya's answer, I see that we have $$P(X_s\le Y_t\text{ simultaneously for all rationals }s\le t) = 1.$$ How could...
2022-07-25 15:53:42