Geodesic
Correction of metrics
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XX, Tome 390 (2011), pp. 201-209

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ZNSL_2011_390_a7,
     author = {P. B. Zatitskiy and F. V. Petrov},
     title = {Correction of metrics},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {201--209},
     publisher = {mathdoc},
     volume = {390},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_390_a7/}
}
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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/