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On Total Masses of Balayaged Measures

Published online by Cambridge University Press:  22 January 2016

Masayuki Itô
Masayuki Itô*
Affiliation:
Mathematical Institute Nagoya University
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Beurling and Deny [1], [2] introduced the notion of Dirichlet spaces. They [2] showed the existence of balayaged measures and equilibrium measures in the theory of Dirichlet spaces. In this paper, we shall show that the following equivalence is valid for a Dirichlet space on a locally compact Hausdorff space X.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 30 , August 1967 , pp. 263 - 278
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Beurling, A. and Deny, J.: Espaces de Dirichlet I, Le case élémentaire, Acta Math., 99 (1958), 203–214.Google Scholar
[2] Beurling, A. and Deny, J.: Dirlichlet spaces, Proc. Nat. Acad. U.S.A., 45 (1959) 208-215.Google Scholar
[3] Bochner, S.: Harmonic analysis and the theory of probablity, Berkeley, 1955.Google Scholar
[5] Deny, J.: Sur les espaces de Dirichlet, Sémin. Theorie du potentiel, Paris, 1957.Google Scholar
[4] Deny, J.: Principe complet du maximum et Contractions, Ann. Inst. Fourier, 15 (1965), 259–272.Google Scholar
[6] Elliott, J.: Dirichlet spaces associated with intregro-differential operators Part I, Illinois Math. J., (1965), 87–98.Google Scholar
[7] Itô, M.: Characterizations of supports of balayaged measures, Nagoya Math. J., 28 (1966), 203–230.CrossRefGoogle Scholar