Let be an increasing sequence of integrable function such that on and is integrable.

Show that .

Can anyone help?

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- Sep 7th 2009, 05:52 PMproblemLebesgue Integral
Let be an increasing sequence of integrable function such that on and is integrable.

Show that .

Can anyone help? - Sep 7th 2009, 09:35 PMJose27
Since and and is integrable, then by the Dominated convergence theorem the result follows. This is valid if with Lebesgue measure. I don't know if the DCT holds for arbitrary measure spaces.