Strong Convergence Theorems for Arbitrary Sequence Series of B-Valued Random Variables

Based on martingale theory in Banach space, using the limit theorem of the B-valued martingale difference sequence, a strong limit theorem for arbitrary sequence series of B-valued random variables is obtained. In addition, according to Radon-Nikodym property of real number space, the main result of this paper contains some well known conclusions in the real number space.