\comment{
Define a map $\sigma':K\to \R^n$ by just taking one of 
$\sigma_i$ and $\overline{\sigma}_i$ when $i>r$ (i.e., when
$\sigma_i$ is complex), so
\[
\sigma'(x) = (\sigma_1(x),\ldots,\sigma_r(x),
\sigma_{r+1}(x),\sigma_{r+3}(x), \ldots),
\]
where we have reordered the $\sigma_I$ so that $\sigma_{m+1}$ is the
conjugate of $\sigma_m$ for $m=r, r+2, \ldots$, and we identify $\C$
with $\R^2$.  Then $\sigma'$ defines an isomorphism from $K\tensor_\Q
\R$ to $\R^n$, and hence a canonical measure on $K\tensor_\Q$.  
}
