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Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. A key concept to describe uncertain quantity is uncertain variable. Uncertainty distribution is an important tool to specify an uncertain variable. In this paper, a sufficient and necessary condition of uncertainty distribution is proved to show what function is an uncertainty distribution. and an example is given on how to construct an uncertain measure with respect to a given function.

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