Find a sequence of integrable functions ( u n ) n N ( u n )
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Find a sequence of integrable functions (un)n∈N with un(x)→u(x) for all x and an integrable function u but such that limn→∞∫undμ≠∫udμ. Does this contradict Lebesgue's dominated convergence theorem (Theorem 12.2 )?
Data from theorem 12.2
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(Lebesgue; dominated convergence) Let (X, A, u) be a measure space and (un)nEN CL () be a sequence of functions such that (a) un(x)
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Consideru x j101x j N It is clear that u is measurable and Lebe...View the full answer
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