On Chung-Teicher type strong law for arrays of vector-valued random variables - Anna Kuczmaszewska (International Journal of Mathematics and Mathematical Sciences)
We study the equivalence between the weak and strong laws of large numbers for arrays of row-wise independent random elements with values in a Banach space ℬ. The conditions under which this equivalence holds are of the Chung or Chung-Teicher types. These conditions are expressed in terms of convergence of specific series and o(1) requirements on specific weighted row-wise sums. Moreover, there are not any conditions assumed on the geometry of the underlying Banach space.