  We consider general Markov chains with discrete time in an arbitrary
measurable (phase) space and homogeneous in time. Markov chains are defined by
the classical transition function which within the framework of the operator
treatment generates a conjugate pair of linear Markov operators in the Banach
space of measurable bounded functions and in the Banach space of bounded finite
additive measures. It is proved that the well-known Doeblin condition $ (D) $
of ergodicity (quasi\-compactness) of the Markov chain is equivalent to the
condition $ (*) $: all finitely additive invariant measures of the Markov
operator are countably additive i.e. there are no invariant purely finitely
additive measures. Under some assumptions, it is proved that the conditions $
(D) $ and $ (*) $ are also equivalent to the condition $ (**) $: the set of
invariant finitely additive measures of a Markov operator is
finite-dimensional. Ergodic theorems are given.
