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How can you prove that if $\mu$ and $\nu$ are finite measures and $n$ is a positive real number, then $\mu$+$n\nu$ is again a finite measure? Is that the same for $\sigma$-finite measures?

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    @kahen Okay. But how would that make any difference? If they are signed they still map $X$ to a real number and therefore the sum is also finite.2012-11-25

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