Summary: Math 501. 3­rd Homework. Due Monday, October 15, 2007.
Homework on the "Lebesgue Measure".
Name: ...............................................................................................................................................
1. (Extended dominated convergence theorem) Let {fn}
n=1 and let {gn}
n=1 be two se-
quence of measurable functions on the measure space (, F, µ). Suppose that:
(i) For each , |fn()| gn().
(ii) For each , lim
n
fn() = f().
(iii) For each , lim
n
gn() = g().
(iv) lim
n
gn() dµ() =

g() dµ().
(v)

Source: Arcones, Miguel A. - Department of Mathematical Sciences, State University of New York at Binghamton

Collections: Mathematics