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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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    Are you sure that $n$ could be any real number?2012-11-25
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    I'm confused: if you are given that $\mu (X) = K$ and $\nu (X) = K'$ then $\mu(X) + n \nu (X) = K + n K'< \infty$. What am I missing?2012-11-25
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    And you probably mean $n \in \mathbb R_{\ge 0}$.2012-11-25
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    @MattN. they could be signed measures, I suppose. [Wikipedia/ba space](https://en.wikipedia.org/wiki/Ba_space).2012-11-25
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    What is/are the axiom/axioms of a measure you have problems to check?2012-11-25
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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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