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 Mar 7 awarded Yearling Jan 24 awarded Popular Question May 11 awarded Popular Question Apr 21 awarded Popular Question Apr 17 awarded Popular Question Apr 15 awarded Nice Question Apr 14 awarded Popular Question Oct 9 awarded Popular Question Jul 2 awarded Curious Jul 2 awarded Inquisitive Mar 25 asked Reaching a level before another for a random walk Mar 25 comment Compact operator maps weakly convergent sequences into strongly convergent sequences @maximumtag what is your definition of weak convergence? Mar 11 accepted Three questions about ucp convergence Mar 11 comment Three questions about ucp convergence Great answer! Thank you so much. Just one small question: For question 1. the second direction you assmued $\epsilon <1$. What about $\epsilon \ge 1$? Or why can we assume w.l.o.g. that for convergence in probability it is enough to consider $\epsilon<1$? Mar 11 revised Three questions about ucp convergence added 61 characters in body Mar 11 asked Three questions about ucp convergence Mar 1 comment $\lim_{h\downarrow 0}\frac{1}{h}\int_{t-h}^tf(s)ds=f(t)$ Thanks for your answer. very nice solution Mar 1 accepted $\lim_{h\downarrow 0}\frac{1}{h}\int_{t-h}^tf(s)ds=f(t)$ Mar 1 comment Proof that the predictable sigma algebra is also generated by continuous and adapted processes thanks for pointing out that in the right continuous case, $Y^n$ is not adapted! Mar 1 accepted Proof that the predictable sigma algebra is also generated by continuous and adapted processes