almost everywhere. In contexts where a measure mu is defined on a space X, a property P(x) holds almost everywhere on X if the set of points n of X for which P(n) does not hold has mu-measure zero. Also we say P(x) for a.a. x in X, standing for almost all x in X.

Sometimes almost everywhere is used in topological spaces where no measure is defined; in this context it usually means that a property holds for all points except for a set of first category, that is, except for a countable union of nowhere dense sets. However it is more common in this case to say that the property holds residually (a residual set being the complement of a set of first category).

Sometimes you see the French version p.p. (for presque partout).