Hello all,

I'm having problems showing this result.

Problem:Let $\displaystyle Z_1, Z_2, ...$ and $\displaystyle Z$ be simple random variables. Show that $\displaystyle Z_n \to Z$ with probability 1 if and only if for all $\displaystyle \epsilon > 0$ there exists an n such that $\displaystyle P(|Z_k - Z| < \epsilon, n \le k \le m) > 1 - \epsilon$ for all m > n.

I haven't made much progress. Hopefully a point in the correct direction will get me going.