On representations of isometric isomorphisms between some monoid of functions
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isometricgroupsisomorphismcanonicallydefinedequipedfunctionsgiven
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We prove that each isometric isomorphism, between the monoids of all nonegative 1-Lipschitz maps defined on invariant metric groups and equiped with the inf-convolution law, is given canonically from an isometric isomorphism between their groups of units.
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