Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-14T12:05:40.862Z Has data issue: false hasContentIssue false
  • English
  • Français

The Topological Support of Gaussian Measure in Banach Space

Published online by Cambridge University Press:  22 January 2016

N. N. Vakhania
N. N. Vakhania*
Affiliation:
Tbilisi University, USSR
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The main result of the present paper is the theorem 1, which describes the topological support of an arbitrary Gaussian measure in a separable Banach space. This theorem will be proved after some discussion of the notion of support itself. But we begin with the reminder of the notion of covariance operator of a probability measure. This notion has a great importance not only for the description of support of Gaussian measures but also for the study of other problems in the theory of probability measures in linear spaces (c.f. [1], [2]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 57 , June 1975 , pp. 59 - 63
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] , , H. H., , 1971.Google Scholar
[2] Vakhania, N. N., On some questions of the theory of probability measures on Banach spaces. Lecture note at Nagoya University, 1973.Google Scholar
[3] Vakhania, N. N., On a property of Gaussian distributions in Banach spaces. Sankhya, The Journal of Indian Statistical Society. Series A, vol. 35 (1973), pp. 23–28.Google Scholar
[4] Sato, H., Gaussian measures on Banach space and abstract Wiener measure. Nagoya Math. J., vol. 36 (1969), pp. 65–81.Google Scholar
[5] , , H. H., O T. II, No. 3, (1966), CTp. 524–528.Google Scholar
[6] Balram S., Rajput, The support of Gaussian measures on Banach spaces. T. 27, No. 4, (1972), CTp. 775–782.Google Scholar
[7] Ito, K., The topological support of Gauss measure on Hilbert space. Nagoya Math. J., vol. 38 (1970), pp. 181–183.Google Scholar
[8] Vachania, N. N., Träger des Gausschen masses im Hilbertraum. Mathem. Nachrichten 64. Band (1974), pp. 319–322.Google Scholar