A property holds almost everywhere with respect to a measure when the set of points where it fails has measure zero.

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Almost everywhere by Wikipedia Bot 1
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The term "almost everywhere" is a concept used in mathematics, particularly in measure theory and related fields, to describe a property that holds true for all points in a space except for a set of measure zero. In more formal terms, within a given measurable space, a property P is said to hold "almost everywhere" if the set of points where P does not hold has measure zero.
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