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However, in this paper we assume that these are not present and it is only required that the input should be a nondecreasing sequence, i.e. we consider the "unconstrained" case.
Let be a nondecreasing sequence in satisfying (3.4).
Let be a nondecreasing sequence of positive numbers.
Let ({b_{n}, ngeq1}) be a nondecreasing sequence of positive numbers.
Let be a nondecreasing sequence of positive reals tending to infinity and and.
Let be a sequence of -mixing random variables satisfying and let be a nondecreasing sequence of positive numbers.
Similar(43)
Since f is nondecreasing it follows that ( x n ) n ∈ ω is a nondecreasing sequence for ⪯.
Then is a nondecreasing sequence.
Hence, { x n } is a nondecreasing sequence.
Obviously, (x n ) is a nondecreasing sequence.
(b If is a nondecreasing sequence with in.
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