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
is a null set
If used for properties of the real numbers, the Lebesgue measure is assumed unless otherwise stated. (The Lebesgue measure is complete.)
Occasionally, instead of saying that a property holds almost everywhere, one also says that the property holds for almost all elements.
The term almost all in addition has several other meanings however.
Here is a list of theorems that involve the term "almost everywhere":