Convergence Of NA Random Matric Sequences And The Theory Of Hsu-Robbins On NA Random Matric Sequences

positively associated(PA) and other sequences are mainly studied initially.Researchresults include:the center limit theory of strong and stable PA sequences,weak andinvariant principle and Berry-Essen theorem on other type of strong stable positivelyassociated sequences.Results on limit theory of NA are few.After 1992,people beginto study almost sure convergence and complete convergence on NA sequence.The concept of negatively associated(NA) random variables is introduced byKumer Joag-dev and Frank-Proschan in the paper[1] in 1983.Recently the limit the-ory of NA random variables has been developed quickly on account of the broadapplication of NA random variables in the mode about reality applies(such as the re-liability theory, the penetration theory and multivariate statistical analysis).A greatmany conclusions consistent to independent situation have been obtained.But neg-ative association has one distinct advantage over the other known types of negativedependence.Increasing functions of disjoint sets of NA random variables are alsoNA.Therefore,the corresponding results are improved.Complete convergence,stronglarge numbers,the iterated logarithm,inequality of NA sequences are studied in pa-per [4-7].In this paper,NA sequences are extended to NA random matric sequences.Onthe base of [4],we establishes a probability inequality and a series of moment inequal-ities for NA random matric sequences.Subsequently,we use the five inequalities tostudy convergence in probability, L_p convergence ,complete convergence and almostsure convergence respectively under the different condition.At last,the theory ofHsu-Robbins which are initiated by Xu Baolu and Robbins in 1946 is developedfurther.We establish similarity results of NA random matric sequences,and prove itstrictly.