Please help me with this problem!
Let $(\Omega,\cal F, \mu)$ be a measure space on which $(f_n)$ is a sequence of bounded, measurable, real-valued functions converging uniformly to $f$.
If the measure of $W$ is finite, the integral of $f_n$ on $\Omega$ converges to the integral of $f$ on $W$. (Should I use monotone convergence THM or dominance convergence THM or neither?)
Show by an example that if the finite-measure hypothesis is dropped then the conclusion may fail.