  Consider a catalytic super-Brownian motion $X=X^\Gamma$ with finite variance
branching. Here `catalytic' means that branching of the reactant $X$ is only
possible in the presence of some catalyst. Our intrinsic example of a catalyst
is a stable random measure $\Gamma $ on $R$ of index $0< gamma <1$.
Consequently, here the catalyst is located in a countable dense subset of $R$.
Starting with a finite reactant mass $X_0$ supported by a compact set, $X$ is
shown to die in finite time. Our probabilistic argument uses the idea of good
and bad historical paths of reactant `particles' during time periods
$[T_{n},T_{n+1})$. Good paths have a significant collision local time with the
catalyst, and extinction can be shown by individual time change according to
the collision local time and a comparison with Feller's branching diffusion. On
the other hand, the remaining bad paths are shown to have a small expected mass
at time $T_{n+1}$ which can be controlled by the hitting probability of point
catalysts and the collision local time spent on them.
