Find a sequence of integrable functions ( u n ) n N ( u n )

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Find a sequence of integrable functions (un)nN with un(x)u(x) for all x and an integrable function u but such that limnundμudμ. Does this contradict Lebesgue's dominated convergence theorem (Theorem 12.2 )?

Data from theorem 12.2

(Lebesgue; dominated convergence) Let (X, A, ) be a measure space and (un)neN CL () be a sequence of

Proof From uw we get ul-limo un

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