November 17, 2025MathematicsOpen Access

General Markov Chains: Dimension of the Space of Invariant Finitely Additive Measures and Their Ergodicity—Problematic Examples

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Quantitative analysis identifies issues with finitely additive measures in Markov chains, complicating ergodic property proofs.
A methodology was demonstrated that employs finitely additive measures for detailed analysis of non-simple properties.
The Markov chain transition function generates operators that play crucial roles in the theory, particularly T, A, and T*.
Results highlight the connection between the properties of measures and the quasi-compactness of the Markov chains.

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Analysis shows invariant finitely additive measures in general Markov chains, indicating complexities in ergodicity proof methodologies.

Alexander Zhdanok (2025) studied this question.

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