Convergence of measures

Convergence of measures describes how a sequence of probability measures (or distributions) becomes closer to a specific measure as the sequence progresses. Think of it as observing a series of patterns or distributions that, over time, increasingly resemble a target pattern. In practical terms, as the sequence advances, the probability of events under these measures approaches the probability of the same events under the limiting measure. This concept is fundamental in probability and statistics, especially in understanding how sample distributions approximate theoretical models or how data-driven estimates settle towards expected values.