I'm working on the following problem for a probability class.

Let be independent random variables with a common continuous distribution function. Let be the -set where for some pair of distinct integers, and show that .

Part of my problem is that this section we're studying on random variables introduces so many new terms that I haven't been able to see how they work together very well. I understand that means that for any except on a set of probability (measure) 0, but am struggling mostly with the first sentence. I'm not asking for a full fledged solution to the problem, but I would be grateful for any assistance on understanding the interplay between the other terms involved and advice on how to start.