Suppose that for every categorical grammar G, the family P contains a probability mass function p which assigns all the probability mass to that grammar G. By (1), the corresponding stochastic grammar G p assigns probability 1 to the mappings enforced by G, as stated in (7).
the stochastic grammar G p "coincides" with the categorical grammar G and the stochastic typology T P thus "contains" or "extends" the original categorical typology T. In this special case, we obviously expect the stochastic , as desired.