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I am trying to understand the given proof below. But I don't really understand how the Theorem of Dominated convergence is applied?

dfv

Which is the function that "dominates" the sequence? and we need to know that this funcion is Lebesgue integrable. There is no such function (explicitly) given.

Nebo Alex
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Dan
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    As $f$ is bounded there is a number $M$ such that $|f(x)|\le M$ for all $x\in[a,b]$. Use the constant function $\varphi(x)=M$ for all $x\in[a,b]$ as your dominating function. – John Dawkins Jan 19 '16 at 16:58

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