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?
Are you sure that $n$ could be any real number? –  Stefan Hansen Nov 25 '12 at 17:18
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? –  Matt N. Nov 25 '12 at 17:23
And you probably mean $n \in \mathbb R_{\ge 0}$. –  Matt N. Nov 25 '12 at 17:24