# Convergence integral problem

1. Oct 6, 2013

### aaaa202

1. The problem statement, all variables and given/known data
I have the attached file as an exercise for class. Problem is that I don't really understand why my book spends so much into solving it, when for me it seems pretty easy.

2. Relevant equations
Lebesgue dominated convergence theorem

3. The attempt at a solution
I thought that since the integrals of g and G are finite they are integrable. Also f_k is integrable for all k. Since f_k is squeezed between g_k and G_k we must have that either lfl≤lGl, which is integrable
or
lfl≤lgl
So lfl is no matter what bounded by an integrable function and we can use the Lebesgue dominated convergence theorem. Why is this not a correct approach?
Is it because finite integral does not imply integrability? I don't see why it wouldn't.

#### Attached Files:

• ###### exercise.pdf
File size:
59 KB
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