dominated convergence theorem

Let X be a measure spaceMathworldPlanetmath, and let Φ,f1,f2, be measurable functionsMathworldPlanetmath such that XΦ< and |fn|Φ for each n. If fnf almost everywhere, then f is integrable and


This theorem is a corollary of the Fatou-Lebesgue theorem.

Title dominated convergence theorem
Canonical name DominatedConvergenceTheorem
Date of creation 2013-03-22 13:12:47
Last modified on 2013-03-22 13:12:47
Owner Koro (127)
Last modified by Koro (127)
Numerical id 13
Author Koro (127)
Entry type Theorem
Classification msc 28A20
Synonym Lebesgue’s dominated convergence theorem
Related topic MonotoneConvergenceTheorem
Related topic FatousLemma
Related topic VitaliConvergenceTheorem