Encyclopedia > Almost everywhere

  Article Content

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 is a subset of some null set. If the measure involved is complete, then the set of elements for which the property does not hold 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 therm "almost everywhere":

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
U.S. presidential election, 1804

... U.S. Office of the Federal Register (http://www.archives.gov/federal_register/electoral_college/scores.html#1804) (Larger version) See also: President of the ...

This page was created in 23.3 ms