In this note we establish the central limit theorem for $\rho$-mixing sequences under combinations of moment assumptions and $\rho$-mixing rates. These results contain the well-known Ibragimov theorems and answer a problem from recent work of Bradley.
"On the Central Limit Theorem for $\rho$-Mixing Sequences of Random Variables." Ann. Probab. 15 (4) 1387 - 1394, October, 1987. https://doi.org/10.1214/aop/1176991983