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Capacitability of Analytic Sets

Published online by Cambridge University Press:  22 January 2016

Masanori Kishi
Masanori Kishi*
Affiliation:
Mathematical Institute, Nagoya University
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Let Ω be a locally compact separable metric space and let Ф be a positive symmetric kernel. Then the inner and outer capacities of subsets of Ω are defined by means of Ф-potentials of positive measures in the following manner. We define the capacity c(K) of a compact set K in a certain manner by means of Ф-potentials.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 16 , February 1960 , pp. 91 - 109
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1960

References

[1] Smith, N. Aronszajn-K. T.: Functional Spaces and functional completion, Ann. Inst. Fourier, 6 (1956), 125–185.Google Scholar
[2] Bourbaki, N.: Intégration, Paris, 1952.Google Scholar
[3] Choquet, G.: Theory of capacities, Ann. Inst. Fourier, 5 (1955), 131–295.Google Scholar
[4] Choquet, G.: Les noyaux réguliers en théorie du potentiel, C. R. Acad. Sci., Paris, 243 (1956), 635–638.Google Scholar
[5] Fuglede, B.: On the theory of potentials in locally compact spaces, to appear.Google Scholar
[6] Kishi, M.: Inferior limit of a sequence of potentials, Proc. Japan Acad., 33 (1957), 314–319.Google Scholar
[7] Kishi, M.: Capacities of borelian sets and the continuity of potentials, Nagoya Math. Journ., 12 (1957), 195–219.CrossRefGoogle Scholar
[8] Kishi, M.: On the capacitability of analytic sets, Proc. Japan Acad., 35 (1959), 158–160.Google Scholar
[9] Ohtsuka, M.: Les relations entre certains principes en théorie du potentiel, Proc. Japan Acad., 33 (1957), 37–40.Google Scholar
[10] Ugaheri, T.: On the general capacities and potentials, Bull. Tokyo Inst. Tech., 4 (1953), 149–179.Google Scholar