Recent content by Mike.B

Can you tell me more?

What do you mean by "recursion"?

I think You are right!

Define ##B=\{\omega\in \Omega:V(\omega)=\infty\}##? And show ##A\cap B##=0$?

You mean ##\mathbb{P}(V=\infty)=1##?

I got you about (2) [<1/2]

I have difficulty about combining the final results, is there any inequality involved?

What is the relation between almost surely and in probability? How to use here?

##\sum_{j=1}^n X_j## by ##S_j##?

Let ##X_i## are i.i.d. and take -1 and +1 with probability 1/2 each. How to prove ##\lim_{n\rightarrow\infty}{\sum_{i=1}^{n}{X_i} }##does not exsits (even infinite limit) almost surely. My work: I use cauchy sequence to prove it does not converge to a real number. But I do not how to prove it...

I am think what is the structure of generated ##\sigma##-algebra. Let me make it specific. How to represent ##\sigma(\mathscr{A})##, where ##\mathscr{A}## is an algebra. Can I use the elements of ##\mathscr{A}## to represent the element in ##\sigma(\mathscr{A})##?

Suppose ##\mu:\mathcal{F}\rightarrow[0,\infty)## be a countable additive measure on a ##\sigma##-algebra ##\mathcal{F}## over a set ##\Omega##. Take any ##E\subseteq \Omega##. Let ##\mathcal{F}_{E}:=\sigma(\mathcal{F}\cup\{E\})##. Then, PROVE there is a countable additive measure...