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 Mat. Zametki, 2015, Volume 98, Issue 6, Pages 930–936 (Mi mz10977)

On Continuous Restrictions of Measurable Multilinear Mappings

E. V. Yurova

Lomonosov Moscow State University

Abstract: 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 $X$.

Keywords: measurable multilinear form, measurable bilinear form, Gaussian measure, compact embedding, Banach space, Radon probability measure.

 Funding Agency Grant Number Russian Science Foundation 14-11-00196

DOI: https://doi.org/10.4213/mzm10977

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English version:
Mathematical Notes, 2015, 98:6, 977–981

Bibliographic databases:

UDC: 519.2

Citation: E. V. Yurova, “On Continuous Restrictions of Measurable Multilinear Mappings”, Mat. Zametki, 98:6 (2015), 930–936; Math. Notes, 98:6 (2015), 977–981

Citation in format AMSBIB
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\paper On Continuous Restrictions of Measurable Multilinear Mappings
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\jour Math. Notes
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\vol 98
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• http://mi.mathnet.ru/eng/mz10977
• https://doi.org/10.4213/mzm10977
• http://mi.mathnet.ru/eng/mz/v98/i6/p930

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. I. Bogachev, “Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures”, Russian Math. Surveys, 71:4 (2016), 703–749
2. L. M. Arutyunyan, “Absolute Continuity of Distributions of Polynomials on Spaces with Log-Concave Measures”, Math. Notes, 101:1 (2017), 31–38
3. V. Bogachev, O. Smolyanov, Topological vector spaces and their applications, Springer Monographs in Mathematics, Springer, 2017, 456 pp.
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