  General Markov chains in an arbitrary phase space are considered in the
framework of the operator treatment. Markov operators continue from the space
of countably additive measures to the space of finitely additive measures.
Cycles of measures generated by the corresponding operator are constructed, and
algebraic operations on them are introduced. One of the main results obtained
is that any cycle of finitely additive measures can be uniquely decomposed into
the coordinate-wise sum of a cycle of countably additive measures and a cycle
of purely finitely additive measures.We have proved theorems on the conditions
and consequences of consistency cycles of measures with cycles of sets of
states of General Markov chains. A theorem is proved (under certain conditions)
that if a finitely additive cycle of a Markov chain is unique, then it is
countably additive.
