Mean Convergences For Sequence Of Pairwise Independent Random Variables

This paper consists of five chapters and mainly researches the characters and the conclusions of the part sums and the weighted sums of pairwise independent random variable's mean convergences. Analysis the mean convergences based on two sets of the sequence of pairwise independent random variables sequence in the conditions of {|ank|r}-uniform integrability and the limit of the sum of the probability is zero. Also analysis the mean convergences in the background of two sets of the sequence of pairwise independent random variables combined with integer sequence which meet the condition of r-th Cesaro uniform integrability and the limit of the sum of the probability is zero. Based on this four cases of pairwise independent random variables, we have the conclusions about mean convergences.