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Aug
15
comment Prove this group $G$ is abelian
@MartinBrandenburg Thank you!
Aug
15
asked Prove this group $G$ is abelian
Aug
14
comment subgroups of finitely generated groups with a finite index
@mez It can be proved this $t$ is exactly $t_1=1$
Aug
12
comment Is group in which every $a$ satisfies $a^3=e$ abelian?
@ZhenLin Thank you!
Aug
12
asked Is group in which every $a$ satisfies $a^3=e$ abelian?
Jul
31
comment Manifold has uncountable many smooth stuctures if it has one
@AnthonyCarapetis I think you are right. Would you please coppy your comment as an anwser so I can accept it. Thank you!
Jul
30
asked Manifold has uncountable many smooth stuctures if it has one
Jul
30
comment the equivalence between paracompactness and second countablity in a locally Euclidean and $T_2$ space
Have you got the answer? I am also curious about this problem.
Jul
30
revised exercise 1.21 of chapter 1 of Revuz and Yor's
edited tags
Jul
29
asked exercise 1.21 of chapter 1 of Revuz and Yor's
Jul
26
accepted Exercise 1.13 of chapter 1 of Revuz and Yor's
Jul
26
comment Exercise 1.13 of chapter 1 of Revuz and Yor's
It can also use Fatou's lemma to prove $P(\varlimsup_{t\to+\infty}B_t/\sqrt{t}>0)\geq \varlimsup P(B_t/\sqrt{t}>0)=1/2>0$ and use Kolmogorov or HS 0-1 law. For 2, using the same reasoning we can prove $P(\varlimsup_{t\to+\infty}B_t/\sqrt{t}=+\infty)=P(\varliminf_{t\to-\infty}B_t/ \sqrt {t}=-\infty)=1$ and complet the proof.
Jul
25
comment Exercise 1.13 of chapter 1 of Revuz and Yor's
Thank you! I found my proof of 1 is wrong: $t_0$ should depend on $\omega$.
Jul
25
asked Exercise 1.13 of chapter 1 of Revuz and Yor's
Jul
17
comment How do you prove a CW complex is locally path connected
Dear @RyanBudney I saw this problem in Lee's book where he haven't introduce the conception of contractible. Can you tell me how to prove it directly? Thank you!
Jul
11
revised Product of independent continuous local martingales is local martingale
edited tags
Jul
11
comment Product of independent continuous local martingales is local martingale
@saz The book only said the independent means the natural fields generated by $M$ $N$ respectively are independent. I think $M$ $N$ are with respect to a same filtration wich is larger than the natural filtrations they generated respectively.
Jul
11
asked Product of independent continuous local martingales is local martingale
Jul
2
awarded  Curious
Jun
30
comment an inequality about self-similar process
There's a typo. The oringinal problem is to prove $P(c_p(X_1^{\ast})^p\geq a)\leq P(S_p\geq a)$