Moment complete convergence for B-valued random elements;

Convergence for sequence of B-valued random elements;

The author proves, at first, that the convergence almost-everywhere for a sequence of B-valued random elements is equivalent to its convergence almost-uniformly and then, gives a theorem of Lusin–type declaring that every B-valued random element can be approximated almost uniformly by a sequence of continuous functions.

In this paper, we study application of the small ball condition in the law of the iteratedn Logarithm with B-valued random elements, and we give some results of the law of the iterated Logarithm for i.

In this paper,the weak law of large numbers for arrays of random elements in Banach spaces under uniform intergrability in the Cesàro sence are investigated and geometrical characterization of Banach spaces are discribed.

Some strong convergence for the sequence of B-valued random variables;

In this paper,under the condition of uniformly boundary tail probability,we discuss the strong convergence for Jamison weighted sums of independent and differently distributed B-valued random variables.