Going beyond the special cases so far described, the greatest potential for modelling with unnormalized families of densities is achieved by freeing oneself from these limitations. Any family of nonnegative functions on the state space can be used to specify a model so long as all of the functions can be proved to be integrable and not almost everywhere zero so that the normalizing function is finite and nonzero. This permits tremendous and largely unexplored flexibility in specifying models with complex dependence.