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).

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