  The paper is concerned with constructing pairwise dependence between $m$
random density functions each of which is modeled as a mixture of Dirichlet
process model. The key to this is how to create dependencies between random
Dirichlet processes. The present paper adopts a plan previously used for
creating pairwise dependence, with the simplification that all random Dirichlet
processes share the same atoms. Our contention is that for all dependent
Dirichlet process models, common atoms are sufficient.
  We show that by adopting common atoms, it is possible to compute the $L_p$
distances between all pairs of random probability measures.
