Convergence Of Uncertain Variable Sequences

The research work in this thesis is uncertain theory, the convergence of uncertain variable sequences is the main topics of this thesis.First of all, the definitions that uncertain variable sequence is mean fundamental and that the terms of finite valued set functions are uniformly absolutely continuous with respect to uncertain measure are given. Then, the necessary and sufficient condition of that uncertain variable sequence is mean fundamental is obtained. Next, the concept uncertain measure is upper continuous at zero set is introduced. According to this concept, the necessary and sufficient conditions of both uncertain variable sequence is convergence almost surely implies convergence uniformly almost surely and uncertain variable sequence is convergence almost surely implies convergence in measure are obtained also.Secondly, the definitions that Cauchy convergence almost surely of uncertain variable sequence and upper continuous of uncertain measure are introduced. Sequentially, the necessary and sufficient conditions of Cauchy convergence almost surely of uncertain variable sequence are received. Apart from this, the sufficient conditions of that uncertain variable sequence is convergence almost surely, uncertain variable sequence is Cauchy convergence in uncertain measure, uncertain variable sequence is convergence uniformly almost surely are proved.Thirdly, a kind of undecrease dual function is investigated in the uncertain spaces. Then, some equivalent conditions of convergence in uncertain measure are given based on that function.