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In this paper, we discuss some properties in uncertainty theory when uncertain measure is continuous. Firstly, the judgement conditions of continuous uncertain measure are proposed. Secondly, basic properties of uncertainty distribution and critical values of uncertain variable are proved. Finally, the convergence theorems for expected value are discussed.

The additivity axiom of classical measure theory has been challenged by many mathematicians. Different replacements of the additivity correspond with different theory. In uncertainty theory, the additivity is replaced with self-duality and countable subadditivity. Similar to classical measure theory, there are some properties studied in uncertainty theory. Given the measure of each singleton set, the measure can be fully and uniquely determined in the sense of the maximum uncertainty principle. Generally speaking, a product uncertain measure may be defined in many ways, in this paper, a kind of definition is proposed.

For uncertain variable sequences, conditions of convergences such as Cauchy convergence in measure, convergence almost surely and convergence uniformly almost surely are given. Consequently, the relationships among convergences of uncertain variable sequences are shown. These results have not been proposed in literature so far.

In this treatise, we define statistically pre-Cauchy sequences of complex uncertain variable for five cases of uncertainty viz., in mean, in measure, in distribution, in almost surely and in uniformly almost surely and we confine our study to statistically pre-Cauchy sequence in mean, in measure and in distribution only. Furthermore, we establish the relationship between statistically pre-Cauchy and statistically convergent sequence by using complex uncertain variables. Finally, we initiate the study of statistically pre-Cauchy sequences of complex uncertain variables via Orlicz functions also.