almost everywhere

In measure theory (a branch of mathematical analysis), one says that a property holds almost everywhere if the set of elements for which the property does not hold is a null set, i.e. is a set with measure zero. If used for properties of the real numbers, the Lebesgue measure is assumed unless otherwise stated. It is abbreviated a. e.; in older literature one can find p. p. instead, which stands for the equivalent French language phrase presque partout.
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