Lebesgue's dominated convergence theorem states that if 
is a sequence of measurable
functions, 
converges pointwise
to 
almost everywhere as
,
and 
for all 
, where 
is Lebesgue integrable,
then 
is Lebesgue integrable,
and
 |
Lebesgue's Dominated Convergence Theorem
See also
Almost Everywhere Convergence, Measure Theory, Pointwise ConvergenceExplore with Wolfram|Alpha
References
Browder, A. Mathematical Analysis: An Introduction. New York: Springer-Verlag, 1996.Referenced on Wolfram|Alpha
Lebesgue's Dominated Convergence TheoremCite this as:
Weisstein, Eric W. "Lebesgue's Dominated Convergence Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LebesguesDominatedConvergenceTheorem.html