I'm taking a course next semester at my university on applied probability (with relevance to signal and information theory).
Although the nature of probability is mostly problem solving and applying different models to different cases and maybe occasionally derive something from scratch, I have this feeling that I will most definitely be missing out the some of the results from pure math that underlies ideas in probability, therefore, nothing gets glued together at the end and I'll just wind up forget everything I've learned in a month or two.
One of which would be sigma algebra, something I'm tackling at the moment.
Thus in your opinion, what would be some of the most important results from pure math that a student would need to know for taking a course in probability?