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Let $\mu$ be a positive measure, $f$ be an extended $\mu$-integrable function. Define the set function $\nu$ on $\mathcal{M}$ by $$ \nu(E):=\int_E f~\text{d}\mu\qquad E\in \mathcal{M}.$$ I need assistance in showing that $\nu$ is signed measure.

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    For countable additivity, try the dominated convergence theorem.2012-01-25
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    What part of the proof that $\nu$ is a signed measure trips you up? You have to show three things. What are they?2012-01-25
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    @tomcuchta: I have two of them done. I'm struggling with the countable additivity part...2012-01-25

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