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Zapiski Nauchnykh Seminarov POMI, 2011, Volume 390, Pages 201–209
(Mi znsl4551)
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This article is cited in 12 scientific papers (total in 12 papers)
Correction of metrics
P. B. Zatitskiyab, F. V. Petrovb a Saint-Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Abstract:
We prove that a symmetric nonnegative function of two variables on a Lebesgue space that satisfies the triangle inequality for almost all triples of points is equivalent to some semimetric. Some other properties of metric triples (spaces with structures of a measure space and a metric space) are discussed.
Key words and phrases:
Lebesgue space, semimetric.
Received: 01.10.2011
Citation:
P. B. Zatitskiy, F. V. Petrov, “Correction of metrics”, Representation theory, dynamical systems, combinatorial methods. Part XX, Zap. Nauchn. Sem. POMI, 390, POMI, St. Petersburg, 2011, 201–209; J. Math. Sci. (N. Y.), 181:6 (2012), 867–870
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https://www.mathnet.ru/eng/znsl4551 https://www.mathnet.ru/eng/znsl/v390/p201
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Abstract page: | 429 | Full-text PDF : | 113 | References: | 49 |
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