On some relations between the Martin boundary and the Feller boundary

Hisao WATANABE

doi:10.2969/jmsj/01320189

Hisao WATANABE

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JOURNAL FREE ACCESS

1961 Volume 13 Issue 2 Pages 189-196

DOI https://doi.org/10.2969/jmsj/01320189

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Published: 1961 Received: November 09, 1960 Available on J-STAGE: August 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: August 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) N. Bourbaki, Éléments de mathématique, 3, Topologie générale, Paris, 1948.
2) J. Dixmier, Sur certains espaces considérés par M. H. Stone, Summa Brasil Math., 2(1951), 152-182.
3) J. L. Doob, Discrete potential theory and boundaries, J. Math. Mech., 8(1959), 433-455.
4) N. Dunford and J. T. Schwarz, Linear operators, New York, 1958.
5) W. Feller, Boundaries induced by non-negative matrices, Trans. Amer. Math. Soc., 83 (1956), 19-54.
6) W. Feller, On boundaries and lateral conditions for the Kolmogorov differential equations, Ann. Math,, 65 (1957), 527-570.
7) P. R. Halmos, Measure theory, New York, 1950.
8) K. Ito, Stochastic process, Tata Institute notes, Bombay, 1960.
9) D. G. Kendall, Hyperstonian spaces associated with Markov chains, Proc. London Math. Soc., 10 (1956), 67-87.
10) M. A. Naimark, Normed rings, 1959.
11) M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41(1937), 375-481.
12) T. Watanabe, Some topics related to Martin boundaries induced by countable Markov processes, I. S. I., 32 ses. Tokyo, 1960.
13) T. Watanabe, On the theory of Martin boundaries induced by countable Markov processes, Mem. Coll. Sci. Kyoto, 33 (1960), 39-108.

Right : [1] N. Bourbaki, Éléments de mathématique, 3, Topologie générale, Paris, 1948.
[2] J. Dixmier, Sur certains espaces considérés par M. H. Stone, Summa Brasil Math., 2 (1951), 152-182.
[3] J. L. Doob, Discrete potential theory and boundaries, J. Math. Mech., 8 (1959), 433-455.
[4] N. Dunford and J. T. Schwarz, Linear operators, New York, 1958.
[5] W. Feller, Boundaries induced by non-negative matrices, Trans. Amer. Math. Soc., 83 (1956), 19-54.
[6] W. Feller, On boundaries and lateral conditions for the Kolmogorov differential equations, Ann. Math,, 65 (1957), 527-570.
[7] P. R. Halmos, Measure theory, New York, 1950.
[8] K. Ito, Stochastic process, Tata Institute notes, Bombay, 1960.
[9] D. G. Kendall, Hyperstonian spaces associated with Markov chains, Proc. London Math. Soc., 10 (1956), 67-87.
[10] M. A. Naimark, Normed rings, 1959.
[11] M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41 (1937), 375-481.
[12] T. Watanabe, Some topics related to Martin boundaries induced by countable Markov processes, I. S. I., 32 ses. Tokyo, 1960.
[13] T. Watanabe, On the theory of Martin boundaries induced by countable Markov processes, Mem. Coll. Sci. Kyoto, 33 (1960), 39-108.

Date of correction: August 29, 2006 Reason for correction: - Correction: PDF FILE Details: -

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