  Generalized Bratteli diagrams with a countable set of vertices in every level
are models for aperiodic Borel automorphisms. This paper is devoted to the
description of all ergodic probability tail invariant measures on the path
spaces of generalized Bratteli diagrams. Such measures can be identified with
inverse limits of infinite-dimensional simplices associated with levels in
generalized Bratteli diagrams. Though this method is general, we apply it to
several classes of reducible generalized Bratteli diagrams. In particular, we
explicitly describe all ergodic tail invariant probability measures for (i) the
infinite Pascal graph and give the formulas for the values of such measures on
cylinder sets, (ii) generalized Bratteli diagrams formed by a countable set of
odometers, (iii) reducible generalized Bratteli diagrams with uncountable set
of ergodic tail invariant probability measures. We also consider the method of
measure extension by tail invariance from subdiagrams. We discuss the
properties of the Vershik map defined on reducible generalized Bratteli
diagrams.
