Let ${\bf \mathfrak{K}}$ be a complex with the set of vertices M and A, B and R three subsets of M. R is said to be separating A and B in ${\bf \mathfrak{K}}$ (notation: $(A\mathop |\limits_R B)\mathfrak{K}$ if any $a \in A$ and $b \in B$ are not connected in $ \mathfrak{K} - \cup _{r \in R} O_\mathfrak{K} r$ is the star of r in $\mathfrak{K}$.Let $S_a ,a \in M$, be a finite set and $S_A = \prod _{a \in A} S_a ,A \subset M$. A measure $\mu _M $ on $S_M $ is said to be Markov relative to $\mathfrak{K}$ if for any separation $(A\mathop |\limits_R B)\mathfrak{K}$ if any $a \in A$ and $a \in A$ and $x_R \in S_R $ the inequality, $\mu _M (x_R ) \ne 0$ implies \[ \mu _M \left(X_A \times X_B |x_R \right) \ne \mu _M \left(X_A |x_R \right)\mu _M \left(X_B |x_R \right) \]for arbitrary $X_A \subset S_A $ and $X_B \subset S_B $.Theorem. If the complex $\mathfrak{K}$ is regular, any consistent family of measures $\mu _\mathfrak{K} = \left\{ {\mu _K } \right\}_{K \in \mathfrak{K}} $ on $S_\mathcal{K} = \left\{ {S_K } \...