Decomposition of Finitely Additive Markov Chains in Discrete Space

In this study, we consider general Markov chains (MC) defined by a transition probability (kernel) that is finitely additive. These were constructed S. Ramakrishnan within the concepts and symbolism of game theory. Here, study these MCs using operator approach. our work, state space (phase space) MC has any cardinality sigma-algebra discrete. The construction phase allows us to decompose kernel (and operators it generates) into sum two components: countably additive purely kernels. We show atomic. Some properties with their invariant measures are also studied. A class combined its subclasses introduced, proven. asymptotic regularities such revealed.