Abstract: Strong laws of large numbers for weighted sums of independent random variables are proved for Banach spaces of type . Chen, Zhu and Fang's (1996) results on real-valued i.i.d. random variables are extended and generalized, and their unsolved problem is answered. Also, necessary conditions for these strong convergences are considered.
Key words and phrases: Banach space of type , random element, strong law, weighted sum.