Almost Everywhere Convergence is a concept in probability and analysis that describes the behavior of a sequence of functions. A sequence of functions f_n converges to a function f almost everywhere if, for most points in the domain, the sequence approaches the function as n increases. Specifically, the set of points where the convergence does not occur must have a measure of zero. This means that while there may be some exceptions, they are negligible in terms of size. In practical terms, almost everywhere convergence is useful in various fields, including measure theory and functional analysis, as it allows for the interchange of limits and integrals under certain conditions.