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.