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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2011 Volume 390, Pages 201–209 (Mi znsl4551)

This article is cited 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.

UDC: 517.518.115+517.987.1+515.124.4

Received: 01.10.2011


 English version:
Journal of Mathematical Sciences (New York), 2012, 181:6, 867–870

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