Complete Convergence for ρ-mixing Sequences

Let l （x） andβ（x） be even positive fun（?）tions. Suppose there is a censtant θ>0 such that β（x）/x, x/β（x） and l（x） （x>0） are monotone nondecreasing Denote α（x） is the converse funotion of β（x）. Theerem 1 Suppose there is a constant 0<ε<1 such that β（x）l(β（x）)/x and x/(β（x）l(β（x）)) are monotene nondecreasing. Let {X} be a ρ-mixing sequence of identically distributed random varibles with EX=0 and Eβ（X）l(β（|X|）)