Feng
  • Member for 3 years, 1 month
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  • China
1 answers
7 votes
241 views
3 bookmarks
Does $H\leq G$ imply $[G_x: H_x]\leq [G: H]$?
1 answers
7 votes
336 views
6 bookmarks
A random series has infinitely many zeros in $[0,1)$ almost surely.
1 answers
6 votes
217 views
4 bookmarks
Construct probability measures to get the desired probability distributions of random variables.
0 answers
5 votes
53 views
3 bookmarks
$K(x,t)=2\pi\sum_{n=1}^\infty n\sin(n\pi x)e^{-n^2\pi^2t}$ satisfies some "pesudo-good-kernel" properties
1 answers
5 votes
193 views
4 bookmarks
A Gronwall-type inequality for $L^p$ norms
1 answers
5 votes
99 views
1 bookmarks
The composition space of $L^p$ spaces is complete.
1 answers
5 votes
115 views
3 bookmarks
Suppose $f\in L^1(\mathbb R)$ satisfies $\int_G f(x)\,dx=\int_{\bar{G}}f(x)\,dx\ \ \text{for all open set } G\subset\mathbb R$, then $f=0$ a.e.
2 answers
4 votes
79 views
Asymptotic behavior of $\sum_{r=0}^\infty r\left[ \left(1-\frac 1{2^{r+1}}\right)^m-\left(1-\frac 1{2^{r}}\right)^m\right]$ as $m\to+\infty$.
2 answers
4 votes
346 views
2 bookmarks
Wald’s identity for Brownian motion with $E[\sqrt T]<\infty$.
1 answers
3 votes
53 views
$L^1$ estimate about a kind of fourier restriction type function
0 answers
3 votes
90 views
2 bookmarks
Maximum principle for $-\Delta u=(u-1)(u+1)$
2 answers
2 votes
78 views
A stronger result about Implicit Function Theorem: Factorization $F(x,y)=G(x,y)(x-g(y))$
0 answers
2 votes
56 views
1 bookmarks
Find a continuous linear functional $f\in(\ell^\infty)^*$ satisfying two requirements.
1 answers
2 votes
171 views
4 bookmarks
An application of Markov property
2 answers
2 votes
102 views
Infinite closed set in $\mathbb{R}$ can be generated by its countable subsets
2 answers
2 votes
339 views
1 bookmarks
Is a harmonic function in $\mathbb{R}^2$ which is $o(\ln |x|)$ a constant?
0 answers
1 votes
29 views
1 bookmarks
$\|\nabla_x(-\Delta_x)^{-1} P_{\leq 1} f\|_{L^p}\lesssim_p\|\langle x\rangle f\|_{L^1}$ for all mean-zero $f$ and all $p\in(1,\infty]$.
1 answers
1 votes
45 views
2 bookmarks
Whether the optional stopping theorem is true for a positive continuous martingale and integrable stopping times
1 answers
1 votes
31 views
1 bookmarks
convergence of the condtional expectation with the conditional $\sigma-$fields change
1 answers
1 votes
24 views
$E\in \mathcal{B}(H)$ is a nontrivial projection, then $\mathcal{A}=\{\alpha E:\alpha\in \mathbb C\}$ is weakly closed.
1 answers
1 votes
67 views
The right-continuity property of a filtration is preserved when adding the class of negligible sets.
0 answers
0 votes
44 views
Generator of the semigroup associated with the integral operator by Gaussian kernel
1 answers
0 votes
53 views
2 bookmarks
$\mathcal{B}$ is maximal Abelian subalgebra iff it concides with its commutant
1 answers
0 votes
102 views
2 bookmarks
If $F$ is purely discontinuous, then $\limsup_{t\to\infty}f(t)=1$.