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I'm trying to solve this question and I need help as to how to start. I realized that one direction is easy but the other, I have tried several times but it yields no results. The question is if $h \in L^+(X, M)$ and $ (X, M, \mu) $ is a measurable space. Let the function $\Lambda :M \rightarrow [0, \infty]$ defined by $ \Lambda (E) = \int _{E}h d \mu$ be a measure. Now, we need to proof that $ (X, M, \Lambda)$ is $\sigma$-finite if and only if $h< \infty$ $\mu$- almost everywhere.

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    And which is the direction that you found easy, and which is the direction that you are having trouble with?2011-11-16
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    If $h \in {h} < \infty$ then $ (X, M, \mu ) $ is $\sigma $- finite. That direction is okay..2011-11-16

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