On the equivalence of integral norms on the space of measurable polynomials witj respect to a convex measure

Vasiliy Berezhnoy

Russia, Moscow State University, Dept. Mechanics and Mathematics, Chair of Theory of Functions and Functional Analysis

Abstract: We prove that, for a convex product-measure $\mu$ on a locally convex space, for any set $A$ of positive measure, on the space of measurable polynomials of degree $d,$ all $L_p(\mu)$-norms coincide with the norms obtained by restricting $\mu$ to $A.$

Keywords: Convex measure, measurable polynomial, equivalent norms.

MSC: 28C20, 60B05

Language: English

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