  General Markov chains with a countably additive transition probability in
arbitrary phase space are considered. Markov operators extend from the space of
countably additive measures to the space of finitely additive measures. In the
author's papers a theorem was earlier proved that if all invariant finitely
additive measures of a Markov chain are countably additive, i.e. there are no
invariant purely finitely additive measures, then their subspace is
finite-dimensional and the Markov chain satisfies the Doob-Doeblin
quasicompactness conditions. In the same paper, a partial inversion of this
theorem was proved with the dimension "one". In this paper we prove the
inversion of this assertion for any finite dimensionality, but under certain
additional conditions. The ergodic consequences are given. Examples and methods
for studying their asymptotics with the aid of invariant purely finitely
additive measures are given.
