  The purpose of the paper is a general analysis of path space
  measures. Our focus is a certain path space analysis
  on generalized Bratteli diagrams. We use this in a systematic study of
systems of self-similar measures (the term ``IFS measures'' is used in the
paper) for both types of such diagrams, discrete and continuous. In special
  cases, such measures arise in the study of iterated function
  systems (IFS). In the literature, similarity may be defined by,
  e.g., systems of affine maps (Sierpinski), or systems of conformal
  maps (Julia). We study new classes of semi-branching
  function systems related to stationary Bratteli diagrams. The
  latter plays a big role in our understanding
  of new forms of harmonic analysis on fractals. The measures
  considered here arise in classes of discrete-time, multi-level
  dynamical systems where similarity is specified between levels.
  These structures are made precise by prescribed systems of
  functions which in turn serve to define self-similarity, i.e., the similarity
of large scales, and small scales.
  For path space systems, in our main result, we give a necessary and
sufficient condition for the existence of such generalized IFS measures. For
the corresponding semi-branching function systems, we further identify the
measures which are also shift-invariant.
