This is the Lebesgue
Dominated Convergence Theorem: it expresses the fact that if {fn}
is a sequence of Lebesgue-integrable functions, all bounded in
absolute value by the same nonnegative integrable function g,
then the limit of the integrals of the fn's is the integral of the limit (which is assumed to
exist pointwise).
REFERENCE:
-
Walter Rudin,
Real and Complex Analysis, Second Edition, New York,
McGraw-Hill, 1966, page 27.
|
