This paper provides L` and weak laws of large numbers for uniformly integrable
L1-mixingales. The L1-mixingale condition is a condition of asymptotic weak temporal dependence
that is weaker than most conditions considered in the literature. Processes covered by the laws of
large numbers include martingale difference, Φ(.), ρ(.) and α(•) mixing, autoregressive moving
average, infinite order moving average, near epoch dependent, L1-near epoch dependent, and
mixingale sequences and triangular arrays. The random variables need not possess more than one
moment finite and the L1-mixingale numbers need not decay to zero at any particular rate. The proof
of the results is remarkably simple and completely self-contained
