This article is cited in 3 scientific papers (total in 3 papers)
On Continuous Restrictions of Measurable Multilinear Mappings
E. V. Yurova
Lomonosov Moscow State University
This article deals with measurable multilinear mappings on Fréchet spaces and analogs of two properties which are equivalent for a measurable (with respect to gaussian measure) linear functional: (i) there exists a sequence of continuous linear functions converging to the functional almost everywhere; (ii) there exists a compactly embedded Banach space $X$ of full measure such that the functional is continuous on it. We show that these properties for multilinear functions defined on a power of the space $X$ are not equivalent; but property (ii) is equivalent to the apparently stronger condition that the compactly embedded subspace is a power of the subspace embedded in $X$.
measurable multilinear form, measurable bilinear form, Gaussian measure, compact embedding, Banach space, Radon probability measure.
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Mathematical Notes, 2015, 98:6, 977–981
E. V. Yurova, “On Continuous Restrictions of Measurable Multilinear Mappings”, Mat. Zametki, 98:6 (2015), 930–936; Math. Notes, 98:6 (2015), 977–981
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\paper On Continuous Restrictions of Measurable Multilinear Mappings
\jour Mat. Zametki
\jour Math. Notes
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L. M. Arutyunyan, “Absolute Continuity of Distributions of Polynomials on Spaces with Log-Concave Measures”, Math. Notes, 101:1 (2017), 31–38
V. Bogachev, O. Smolyanov, Topological vector spaces and their applications, Springer Monographs in Mathematics, Springer, 2017, 456 pp.
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