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A general theorem for decomposition of linear random processes

Author: D. J. Hebert
Journal: Proc. Amer. Math. Soc. 38 (1973), 331-336
MSC: Primary 28A40; Secondary 60G20
MathSciNet review: 0320265
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Abstract: Let $ E$ and $ F$ be locally convex spaces in duality and let $ f$ be a linear random process indexed by $ F$ such that the corresponding cylindrical measure is a Radon measure. It is shown without any assumptions of metrizability or countability that there is an equivalent process with continuous linear trajectories.

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  • [1] Albert Badrikian, Séminaire sur les fonctions aléatoires linéaires et les mesures cylindriques, Lecture Notes in Mathematics, Vol. 139, Springer-Verlag, Berlin-New York, 1970 (French). MR 0279271
  • [2] N. Bourbaki, Éléments de mathématique. Fasc. XXXV. Livre VI: Intégration. Chapitre IX: Intégration sur les espaces topologiques séparés, Actualités Scientifiques et Industrielles, No. 1343, Hermann, Paris, 1969 (French). MR 0276436
  • [3] A. Ionescu Tulcea and C. Ionescu Tulcea, Topics in the theory of lifting, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 48, Springer-Verlag New York Inc., New York, 1969. MR 0276438
  • [4] L. Schwartz, Séminaire Laurent Schwartz--applications radonifiantes, École Polytechnique, Centre de Mathématiques, Paris, 1969/70.

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Keywords: Generalized processes, cylindrical measures, lifting, decomposition
Article copyright: © Copyright 1973 American Mathematical Society

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