  A Bratteli diagram is a type of graph in which the vertices are split into
finite subsets occupying an infinite sequence of levels, starting with a bottom
level and moving to successively higher levels along edges connecting
consecutive levels. An information source on a Bratteli diagram consists of a
sequence of PMFs on the vertex sets at each level that are compatible under
edge transport. By imposing a regularity condition on the Bratteli diagram, we
obtain various results for its information sources including ergodic and
entropy rate decomposition theorems, a Shannon-Mcmillan-Breiman theorem, and
lossless and lossy source coding theorems. Proof methodology exploits the
Vershik transformation on the path space of a Bratteli diagram. Some results
for finite alphabet stationary sequential information sources are seen to be a
special case of the results of this paper.
