The $ L_r $ convergence and weak laws of large numbers for $\widetilde{\rho}$-mixing random variables

Authors

$\widetilde{\rho}$ -mixing, uniform CesÃ ro-type condition,

$L_{r}$ convergence, weak law of large numbers.

The

$L_{r}$ convergence and a class of weak laws of large numbers are obtained for sequences of

$\widetilde{\rho}$ -mixing random variables under the uniform CesÃ ro-type condition. This is weaker than the

$p$ th-order CesÃ ro uniform integrability. doi:10.1017/S1446181117000037