The rates of almost sure conditional complete moment convergence of bootstrap means were considered and its asymptotic behavior was gained;Also the same results for the law of logarithm and iterated logarithm for the moment of bootstrap means were obtained.

This paper presents some almost sure convergence properties and a strong law of large numbers for the partial sum of associated random variable sequences based on the Hajek-Renyi inequality for associated random variables and the Chung-Erdos inequality for event sequences using the Kronecker lemma and the Borel-Cantelli lemma,which generalize and improve the result in related literature.

In the paper,we prove an almost sure convergence for the maximum of stationary Gaussion vector sequencs under the conditons rn(p)log n(log log n)1+ε=O(1),rn(p,q)log n(log log n)1+ε=O(1),1≤p≠q≤d.

Complete convergence and Marcinkiewicz’s strong law and almost sure convergence for -mixing random sequences with different distributions are discussed.

This paper gaves its equivalent propositions and proves that a.

Let B be a separable Banach space, in this thesis, Construct an a.

We proved the existence of the optimal control in the sense of the long run average of the output tracking errors and a.

The paper discusses the relations between complete convergence and almost uniform convergence,almost everywhere convergence,convergence in measure of fathomable functional sequence,and presents two common properties and one decision theorem.

We introduce the concepts of the convergence in fuzzy measures and the almost everywhere convergence for the sequence of measurable fuzzy valued functions in the general fuzzy measure space in this paper.