Abstract
There are two kinds of isometric isomorphism in probabilistic metric space theory. The first is that a PM space (E, F) is isometrically isomorphic to another PM space (E′, F′), and the second is that a PM space (E, F) is isometrically isomorphic to a generating space of quasi-metric family (E′, dr, r∈(0,1)). This paper establishes the connection between the two kinds of isometric isomorphism.
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