# Article

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Keywords:
signed measure; band; Markov operator; asymptotic periodicity of Markov operators; quasi-constructive Markov operator; space of signed measures on a $\sigma$-algebra
Summary:
A new criterion of asymptotic periodicity of Markov operators on $L^1$, established in [3], is extended to the class of Markov operators on signed measures.
References:
[1] N. Bourbaki: Intégration. Hermann. Paгis, 1969. Zbl 0189.14201
[2] N. Dunford J. T. Schwarz: Linear operators. Inteгscience Publishers, New York 1958.
[3] J. Komorník: Asymptotic periodicity of the iterates of Markov operators. Tôhoku Math. Ј., 38 (1986), 15-27. DOI 10.2748/tmj/1178228533 | MR 0826761
[4] J. Komorník A. Lasota: Asymptotic decomposition of Markov operators. Bull. Pol. Ac. Math. 35 (1987), З21-З27. MR 0919219
[5] A. Lasota M. C. Mackey: Pгobabilistic Pгopeгties of Deterministic Systems. Cambridge University Press, Cambridge 1985. MR 0832868

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