5 июл. 2012 г. · Let fn be a sequence of functions such that fn→f in L2(Ω). This means ‖fn−f‖L2(Ω)→0,.

26 мар. 2018 г. · There is no reason to believe that L2-convergence gives any information on P-almost sure convergence. One usual counterexample is the ...

28 апр. 2012 г. · This sequence converges to 0 in Lp but for any x∈(0,1) we have fn(x) is not convergent. However, it is a general fact that one can always ...

28 мар. 2023 г. · Does almost sure convergence implies convergence of the mean? 1 · Almost sure convergence of random variables · 3 · From Cauchy in Measure to ...

7 авг. 2019 г. · It converges in l2 to 0 but does not converge to 0 almost surely. This is because it doesn't agree with 0 on the entire interval of [0,1], every ...

19 дек. 2017 г. · It converges almost surely to 0, but not in L2 and E[X2n]=−n21n=−n<0. Share.

5 дек. 2016 г. · It is a theorem due to Paul Lévy that a series of independent random variables converges almost surely if and only if it converges in ...

20 окт. 2013 г. · For the first question, try P[Xn=0]=1−1/n2, P[Xn=2n]=1/n2, then Xn→0 almost surely but E[Xn] does not converge to 0.

28 сент. 2020 г. · The point is that Ascoli-Arzelá gives uniform convergence of a subsequence to some continuous function, which is completely unknown a priori.

23 мар. 2016 г. · In fact, almost sure convergence does not imply L2-convergence in general: Consider for example fn(x)=n1{0≤x≤1/n2}.