Geodesic
A~fine topology on the entrance boundary
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 1, pp. 131-134

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Markov processes in a countable phase space are considered. On the entrance boundary a fine topology is introduced, the existence of the limit of the arbitrary positive and Green's function ratio being proved. Some applications of the theorem obtained to the general boundary condition problem are described. The definitions introduced and the proofs are easily generalized to the case of an arbitrary Markov process for which the entrance boundary may be constructed. 
@article{TVP_1969_14_1_a12,
     author = {V. L. Mazo},
     title = {A~fine topology on the entrance boundary},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {131--134},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_1_a12/}
}
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V. L. Mazo. A~fine topology on the entrance boundary. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 1, pp. 131-134. http://geodesic.mathdoc.fr/item/TVP_1969_14_1_a12/