Composition of Probability Measures on Finite Spaces
  Decomposable models and Bayesian networks can be defined as sequences of
oligo-dimensional probability measures connected with operators of composition.
The preliminary results suggest that the probabilistic models allowing for
effective computational procedures are represented by sequences possessing a
special property; we shall call them perfect sequences. The paper lays down the
elementary foundation necessary for further study of iterative application of
operators of composition. We believe to develop a technique describing several
graph models in a unifying way. We are convinced that practically all
theoretical results and procedures connected with decomposable models and
Bayesian networks can be translated into the terminology introduced in this
paper. For example, complexity of computational procedures in these models is
closely dependent on possibility to change the ordering of oligo-dimensional
measures defining the model. Therefore, in this paper, lot of attention is paid
to possibility to change ordering of the operators of composition.
