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

Abstract

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 CesA ro-type condition. This is weaker than the \(p\)th-order CesA ro uniform integrability. doi:10.1017/S1446181117000037