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

• Дата: 2008
• Автор: Berezhnoy, V.
• Формат: Стаття
• Мова: English
• Опубліковано: Інститут математики НАН України 2008
• Онлайн доступ: http://dspace.nbuv.gov.ua/handle/123456789/4531
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: On the equivalence of integral norms on the space of measurable polynomials with respect to a convex measure / V. Berezhnoy // Theory of Stochastic Processes. — 2008. — Т. 14 (30), № 1. — С. 7–10. — Бібліогр.: 6 назв.— англ.

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