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"If you want to build a ship, don't drum up the men to gather wood, divide the work, and give orders. Instead, teach them to yearn for the vast and endless sea." (Antoine de Saint Exupéry)


2d
comment Finite additivity in outer measure
You are welcome.
Jul
26
accepted About the $\lim_{n \to+\infty} \frac{1}{n}\int_0^1 \log(1+e^{nf(x)})\,dx$ (Rudin's exercise)
Jul
26
comment About the $\lim_{n \to+\infty} \frac{1}{n}\int_0^1 \log(1+e^{nf(x)})\,dx$ (Rudin's exercise)
Oh, yes I see: you are right. Thanks, Davide, for your precious answer.
Jul
26
revised Convergence in $L^p$ by using Holder's inequality
added 9 characters in body
Jul
26
comment Bounding the integral of a function by the integral of its derivative
I expand my comment into an answer, hope it helps.
Jul
26
answered Bounding the integral of a function by the integral of its derivative
Jul
26
comment Bounding the integral of a function by the integral of its derivative
It is the so called "Poincaré inequality".
Jul
26
answered Finite additivity in outer measure
Jul
26
revised Finite additivity in outer measure
added 32 characters in body
Jul
26
asked On the ODE $x^{\prime\prime}(t)+a(t)f(x(t))=0$
Jul
26
comment Non stationary solutions of the PDE $u_t + u_x = u_{xx}$
@900sit-upsaday Many thanks for your useful comment. I did not know Wirtinger's inequality, it is a nice tool to keep in mind. By the way, the exercise has been given as a problem for the admission to a PhD program: it should not be too hard, but I still do not know how to get it... Thanks.
Jul
25
comment Non stationary solutions of the PDE $u_t + u_x = u_{xx}$
I suppose it means the uniform norm (also called the sup norm).
Jul
25
asked Non stationary solutions of the PDE $u_t + u_x = u_{xx}$
Jul
25
comment About the $\lim_{n \to+\infty} \frac{1}{n}\int_0^1 \log(1+e^{nf(x)})\,dx$ (Rudin's exercise)
Great, thanks! ;)
Jul
25
asked About the $\lim_{n \to+\infty} \frac{1}{n}\int_0^1 \log(1+e^{nf(x)})\,dx$ (Rudin's exercise)
Jul
25
comment If $f_n(t):=f(t^n)$ converges uniformly to continuous function then $f$ constant
Thanks for your reply. I wait if something else also replies.
Jul
24
asked If $f_n(t):=f(t^n)$ converges uniformly to continuous function then $f$ constant
Jul
23
accepted Inequality involving Jensen (Rudin's exercise)
Jul
23
comment Inequality involving Jensen (Rudin's exercise)
Now we have to take $\log$ of both sides and from $\int_E f d\mu \le 1$ we conclude, right? Thank you very much for your help.
Jul
23
asked Inequality involving Jensen (Rudin's exercise)