Let $Z_1, Z_2, ldots, Z_l$ be random set functions or intergrals. Then it is possible to discuss their products. In the case of random integrals, $Z_i$ is a random set function indexed y a family, $G_i$ say, of real valued functions g on $S_i$ for which the integrals $Z_i(g) = smallint gdZ_i$ are well defined. If $g_i = in g_i (i = 1, 2, ldots, l) and g_1 otimes cdots otimes g_l$ denotes the tensor product $g(s) = g_1(s_1)g_2(s_2) cdots g_l(s_l) for s = (s_1, s_2, ldots, s_l) and s_i in S_i$, then we can defined $Z(g) = (Z_1 imes Z_2 imes cdots imes Z_l)(g) = Z_1(g_1)Z_2(g_2) cdots Z_l(g_l)$.