Abstract: We considered the convergence problem of the Jamison type weighted sums of extended negatively dependent (END) random variable sequences in a sub-linear expectation space by using the truncation method, and obtained the convergence of the Jamison type weighted sums of END random variable sequences in a sub-linear expectation space. We extended  almost sure  convergence of Jamison type weighted sums of END  random variable sequences  in probability spaces to sub-linear expectation spaces, and the Jamison theorem was generalized.

Key words: sub-linear expectation, almost sure convergence, Jamison type weighted sum, END random , variable sequence, truncation