Nicolas Essis-Breton
Reputation
1,831
Top tag
Next privilege 2,000 Rep.
 Oct 15 accepted Find an inequality for $\|f\|_p$ when $f=f \chi_E+f\chi_{\tilde E}$ and $m(E)=m(\{x:|f|> 1\})<\infty$ Oct 13 accepted Show $\left\lvert\sum_{k=-n}^n \frac{\sin k t }{k}\right\rvert \le \pi + 2$ for all $n$ and $t$, $t \in [0,2\pi]$ Oct 9 accepted Show $\exists f \in C \ni \|f\|_\infty \le 1$, but it's Fourier series diverges Oct 9 accepted Brownian motion: Show $\lim \sum W_{i} (W_{i+1}-W_{i})=\frac12 W^2_t-\frac12 t$ in probability. Sep 25 accepted Show translation is not continuous in $\text{Lip}_\alpha(T)$ Sep 16 accepted Does $\int_a^b \text{Im}(f(t))e^{int}dt=0$ implies $f=0$ on $[a,b]$ Sep 16 accepted Does the complex conjugate of an integral equal the integral of the conjugate? Aug 29 accepted Find $\displaystyle{\int_C \left(1+ \frac{2}{z}\right) dz}$ , where $C(\theta)= e^{i\theta}, 0 \le \theta \le \pi$ Jun 28 accepted Show $g(a)= \operatorname*{arg}_{b \in B} \, f(a,b)=0$ is continuous when $g(a)$ is single-valued and $f$ continuous Jun 23 accepted Show $f(a)=\operatorname{E} \min(aX,Y)$ is a quasilinear function of $a$ Jun 19 accepted Show $f(x)=\int_E x^tg(t)d\mu(t)$ is continuous when $\mu$ is a general measure Jun 15 accepted Finding the fixed point of a function Apr 12 accepted Show $f \in L^p$ implies there is a set $E$ and a function $g$ for which $f=f\chi_E+g$ with $m(E)<\infty$ and $|g|\le 1$ Mar 6 accepted Brownian motion: hitting time of double barrier vs hitting time of single barrier Feb 19 accepted Show a $\sigma$-algebra contains the Borel sets : with $(a,\infty)$ or $(-\infty,b)$? Feb 17 accepted Show a function is continuous if and only if it is both upper and lower semi-continuous Nov 16 accepted Cesaro mixing time and mixing time: show $t_m(1/4) \le 6s_m(1/8)$ Nov 14 accepted Random walk on connected graph: show $E_vT_w \ne E_wT_v$ Nov 7 accepted Show $X_n {\buildrel p \over \rightarrow} X$ and $X_n \le Z$ a.s., implies $X \le Z$ a.s. Nov 7 accepted Show $\sum\limits_{k=2}^{n}{k \over \ln k} \le {n^2 \over \ln n}$