existence of the Lebesgue measure

Theorem (Lebesgue).

Let B be the Borel σ-algebra (http://planetmath.org/BorelSigmaAlgebra) on the real number line. Then, there is a unique measureMathworldPlanetmath μ on the measurable spaceMathworldPlanetmathPlanetmath (R,B) satisfying


for all real numbers a<b.

Title existence of the Lebesgue measureMathworldPlanetmath
Canonical name ExistenceOfTheLebesgueMeasure
Date of creation 2013-03-22 18:33:12
Last modified on 2013-03-22 18:33:12
Owner gel (22282)
Last modified by gel (22282)
Numerical id 4
Author gel (22282)
Entry type Theorem
Classification msc 28A12
Classification msc 26A42
Related topic LebesgueMeasure
Related topic Measure
Related topic CaratheodorysExtensionTheorem