Prokhorov's theorem

Prokhorov's theorem is a result in probability theory that helps us understand the behavior of sequences of probability measures. Essentially, it states that a set of probability distributions (or measures) is relatively compact if it does not "spread out" too much. In simpler terms, if you have many probability distributions that don't vary wildly, you can find a way to restrict them to a smaller, manageable group that still captures essential characteristics. This is crucial in statistics and probability as it ensures that sequences of probabilities converge nicely under certain conditions, making analysis more robust.