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this paper we choose the state space to be the space of tempered measures(2) M tem := M tem (R) :=n 2 M(R) : h; "i < 1 for all " 2 o:Note that in particular the Lebesgue measure ` belongs to M tem . We let M tem  M(R) inheritthe vague topology of M(R):Suppose that is a stable random measure on R of index 0 <  < 1, i.e. for every measurable" : R ! [0; 1) we have(3) Eexph ; "i	= exp ZR"(x)dx:Almost surely, belongs to M tem : This follows from the...

Strong clumping of super-Brownian motion in a stable catalytic medium