  We study the set S of ergodic probability Borel measures on stationary
non-simple Bratteli diagrams which are invariant with respect to the tail
equivalence relation. Equivalently, the set S is formed by ergodic probability
measures invariant with respect to aperiodic substitution dynamical systems.
The paper is devoted to the classification of measures $\mu$ from S with
respect to a homeomorphism. The properties of these measures related to the
clopen values set $S(\mu)$ are studied. It is shown that for every measure
$\mu$ in S there exists a subgroup G of $\mathbb R$ such that $S(\mu)$ is the
intersection of G with [0,1], i.e. $S(\mu)$ is group-like. A criterion of
goodness is proved for such measures. This result is used to classify the
measures from S up to a homeomorphism. It is proved that for every good measure
$\mu$ in S there exist countably many measures $\{\mu_i\}_{i\in \mathbb N}$
from S such that $\mu$ and $\mu_i$ are homeomorphic measures but the tail
equivalence relations on corresponding Bratteli diagrams are not orbit
equivalent.
