Let be i.i.d random signs, . Let be a sequence of real numbers such that . Show that is almost sure convergent.
By , as . but i dont know how to go from here.
Have you seen the Khintchine-Kolmogorov Convergence Theorem?
It follows directly from that.
I found it online RIGHT out of Chow-Teicher.
http://books.google.com/books?id=mYn...heorem&f=false
I have all three editions of that book.
My copy from 78 is falling apart.
Teicher is my advisor's advisor and I published about 15 times In Chow's journal in Taiwan.
http://en.wikipedia.org/wiki/Yuan-Shih_Chow
(Academia Sinica)
So, I use their book a lot.