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Math 501. 3rd Homework. Due Monday, October 15, 2007. Homework on the "Lebesgue Measure".
 

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, ). 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() d() =

g() d().
(v)

  

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

 

Collections: Mathematics