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Representation of isometric isomorphisms between monoids of Lipschitz functions
MFAT 23 (2017), no. 4, 309-319
We prove that each isometric isomorphism between the monoids of all nonnegative $1$-Lipschitz maps defined on invariant metric groups and equipped with the inf-convolution law, is given canonically from an isometric isomorphism between their groups of units.