On the central limit theorem in $F$-spaces
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- by Werner E. Helm PDF
- Proc. Amer. Math. Soc. 72 (1978), 542-544 Request permission
Abstract:
In this note we improve the known result on the integrability of F-norms with respect to Gaussian measures and obtain a Central Limit Theorem for probability measures on arbitrary separable F-spaces.References
- Alejandro D. de Acosta, Existence and convergence of probability measures in Banach spaces, Trans. Amer. Math. Soc. 152 (1970), 273–298. MR 267614, DOI 10.1090/S0002-9947-1970-0267614-9
- Xavier Fernique, Intégrabilité des vecteurs gaussiens, C. R. Acad. Sci. Paris Sér. A-B 270 (1970), A1698–A1699 (French). MR 266263
- Werner E. Helm, Gaussian random elements in certain Orlicz sequence spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), no. 5, 507–514 (English, with Russian summary). MR 461615
- T. Inglot and A. Weron, On Gaussian random elements in some non-Banach spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 22 (1974), 1039–1043 (English, with Russian summary). MR 385953 Ph. Turpin, Convexités dans les espaces vectoriels topologiques généraux, Thèse, Orsay, 1974.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 542-544
- MSC: Primary 60B12; Secondary 60G15
- DOI: https://doi.org/10.1090/S0002-9939-1978-0509252-9
- MathSciNet review: 509252