Convergence on randomly trimmed sums with a ψ-mixing sample:

where α_n and β_n are integers with 0≤α_n【β_n≤n. For an i.i.d, sequence {X_n}, many authors studied the asymptotic behavior of the trimmed sums T_n. In this note, we try extending the research extent in two directions. First, we assume that {X_n} is φ-mixing.Moreover, α_n and β_n may be positive integer-valued random variables satisfying the convergence of the trimming fractions α_n/n and β_n/n to random variables α and β respectively with 0≤α【β≤1 in some sense. It seems to have not been studied for these two cases. A central limit theorem for this kind of randomly trimmed sum is established. Moreover we also show a strong law of large numbers.