Some Convergence Theorems of Uncertain Sequence

The emphasis in this paper is mainly on some convergence theorems of uncertain sequence. Firstly, five main types convergence concepts of uncertain sequence: convergence almost surely (a.s.), convergence almost uniformly (a.u.), convergence in uncertain measure, convergence in uncertain distribution and convergence in mean square (ms) are proposed. Secondly, several sufficient and necessity conditions and relations among of convergence concepts are presented. Thirdly, Egorov theorem, monotone convergence theorem, Fatou lemma and bounded convergence theorem of expected value for uncertain sequence on continuous uncertainty space are obtained.