  We investigate the traceability of positive integral operators on
$L^2(X,\mu)$ when $X$ is a Hausdorff locally compact second countable space and
$\mu$ is a non-degenerate, $\sigma$-finite and locally finite Borel measure.
This setting includes other cases proved in the literature, for instance the
one in which $X$ is a compact metric space and $\mu$ is a special finite
measure. The results apply to spheres, tori and other relevant subsets of the
usual space $\mathbb{R}^m$.
