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. Bibliography: 4 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 390, 2011, pp. 201–209.
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Zatitskiy, P.B., Petrov, F.V. Correction of metrics. J Math Sci 181, 867–870 (2012). https://doi.org/10.1007/s10958-012-0720-8
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DOI: https://doi.org/10.1007/s10958-012-0720-8