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In this work we prove the \emph(bivariate uniqueness) property of the Logistic fixed-point equation, which arise in the study of the \emph(random assignment problem), as discussed by Aldous (2001). Using this and the general framework of Aldous and Bandyopadhyay (2002), we then conclude that the associated \emph(recursive tree process) is \emph(endogenous), and hence the Logistic variables defined in Aldous' 2001 paper are measurable with respect to the $\sigma$-field generated by the edge weights. The method involves construction of an explicit recursion to show the uniqueness of the associated integral equation.

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