Suppose I have a family of integrable function $f_a$ such that $\int_\Omega f_a
Dominated convergence theorem for singular function
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real-analysis
convergence
lebesgue-integral
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0No. Take $\Omega=(-1,1)$, $f_n=0$ on $|x|<1-1/n$ and arrange matters so that $\int f_n=1$ for all $n$. – 2017-02-10