Geodesic
Correction of metrics
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XX, Tome 390 (2011), pp. 201-209 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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P. B. Zatitskiy; F. V. Petrov. Correction of metrics. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XX, Tome 390 (2011), pp. 201-209. http://geodesic.mathdoc.fr/item/ZNSL_2011_390_a7/

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