Remark

\* If $\mu$ is a positive measure on a locally compact metrizable space $X$, then every Souslin subset $A$ of $X$ is $\mu$-measurable. For if $K$ is any compact subset of $X$, $K \cap A$ is a relatively compact Souslin set, hence is capacitable with respect to $\mu^*$ and consequently $\mu$-integrable. Note that the complement in $X$ of a Souslin set, although not in general a Souslin set, is $\mu$-measurable *.