Recent content by student12s

It would remain to show that such $\lambda$ exists. We can definte the sets A_n=\{\omega\in \Omega: |X(\omega)|<n\}. Since A_n is measurable, as X is a random variable, and A_n \uparrow \{\omega: |X|<+\infty}, we have that \lim P(A_n) = P(\{\omega: |X|<+\infty}. Therefore, for all \epsilon...

I apologize. It was a misunderstanding. I will post in the correct part of the forum. Thanks.

I encounter this question while studying Probability by my own. It's not homework/coursework. The application is understanding properties of distribution functions.

Yes, the triangular inequality yields the contradiction. thanks

I´ve been trying to solve this for some time: Let f: R to R be an increasing on a dense set. Define g(x)=inf_{x<t in D} f(t). Show that continuity of f does not imply continuity of g but uniform continuity of f does imply uniform continuity of g. Any help?

I've been trying to solve the following question: Let X be a random variable s.t. Pr[|X|<+\infty]=1. Then for every epsilon>0 there exists a bounded random variable Y such that P[X\neq Y]<epsilon. The ideia here would be to find a set of epsilon measure so Y would be different than X in that...

Thank you very much. Given your guidance, I think I managed to prove the claim. Let p be the set of point of f where f is right-continuous but not left-continuous and let p be an element of L. Since f is not left-continuous in p, there is \epsilon(p)>0 such that, for all \delta>0, there...

I've been trying to answer the following question: Let f be an arbitrary function of $(-\infty,+\infty)$ and let L be the set of point where f is right-continuous but not left-continuous. Show that L is countable. Any help?