monotone convergence theorem
Remark. This theorem is the first of several theorems which allow us to “exchange integration and limits”. It requires the use of the Lebesgue integral: with the Riemann integral, we cannot even formulate the theorem, lacking, as we do, the concept of “almost everywhere”. For instance, the characteristic function of the rational numbers in is not Riemann integrable, despite being the limit of an increasing sequence of Riemann integrable functions.
|Title||monotone convergence theorem|
|Date of creation||2013-03-22 12:47:27|
|Last modified on||2013-03-22 12:47:27|
|Last modified by||Koro (127)|
|Synonym||Lebesgue’s monotone convergence theorem|
|Synonym||Beppo Levi’s theorem|