Encyclopedia > Borel measure

  Article Content

Borel measure

In mathematics, the Borel algebra is the smallest σ-algebra on the real numbers R containing the intervals, and the Borel measure is the measure on this σ-algebra which gives to the interval [a, b] the measure b - a (where a < b).

The Borel measure is not complete, which is why in practice the complete Lebesgue measure is preferred: every Borel measurable set is also Lebesgue measurable, and the measures of the set agree.



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
Hillbilly

... of the state of West Virginia. This has also led to counties in hillbilly areas with pro-Union names such as Lincoln County or Union County. Country and Western ...