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

where αnand βnare integers with 0≤αn<βn≤n. For an i.i.d, sequence {Xn}, many authors studied the asymptotic behavior of the trimmed sums Tn. In this note, we try extending the research extent in two directions. First, we assume that {Xn} is φ-mixing.Moreover, αnand βnmay be positive integer-valued random variables satisfying the convergence of the trimming fractions αn/n and βn/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.