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I know Lebesgue's dominated convergence theorem holds for Lebesgue measure. But, in general, does it hold for an general measure? For example, I know it holds for the counting measure, so we obtain the LDCT for infinite series.

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    $\begingroup$ yes of course, look at the proof..nothing depends on measure, just Fatou's lemma..which holds for an arbitrary measure $\endgroup$ Nov 9, 2015 at 1:26

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Yes, the theorem is valid for any measure. If you read the proof, nothing is used except countable additivity.

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