
In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities. The notion of almost everywhere is a companion notion to the concept of measure zero. In the subject of probability, which is largely based in measure theory, th...
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http://en.wikipedia.org/wiki/Almost_everywhere

(from the article `metalogic`) ...The intuitive idea in this method is to establish that a sentence is true in the ultraproduct if and only if it is true in `almost all` of the ...
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http://www.britannica.com/eb/a-z/a/51

everywhere in a given set except on a subset with measure zero. Abbr.: a.e.
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https://www.infoplease.com/dictionary/almost-everywhere
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