Abstract: Using a Rosenthal-type inequality for maximum of partial sums for ρ^--mixing random variables, we discussed strong conveigence forρ^--mixing random sequences. And we extended the classical HintchineKolmogorov convergence theorem, Marcinkiewicz strong law of large numbers, and the three series theorem etc. for independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.

Key words: ρ^--mixing sequence, Rosenthal type inequality for maximum, convergence