Almost everywhere convergence

Almost everywhere convergence is a concept in mathematics indicating that, for a sequence of functions, the functions get closer and closer to a specific function at all points except possibly on a set of points that is very small (negligible in measure). In practical terms, it means that as you progress through the sequence, the functions behave like the target function almost everywhere, with only a few exceptions that do not significantly affect overall behavior. This type of convergence is useful in analysis because it allows mathematicians to work with functions that converge practically everywhere, ignoring a small, insignificant subset.