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where is an increasing sequence in such that and.
Since is an increasing sequence,, for and for all.
We note that { ξ k } k = 0 ∞ is an increasing sequence of random variables.
That is, the sequence { M k ( 1 ) } is an increasing sequence.
There is an increasing sequence of positive integers such that and (3.5).
Therefore,, that is, is an increasing sequence and, hence, the limit of exists.
(30) Thus ({tau_{n}(t)}) is an increasing sequence for each (t>0).
Therefore { W k } k = 1 ∞ is an increasing sequence of uniformly bounded convex sets in K.
Indeed, assume that ( ( x n ) ) n ∈ N is an increasing sequence in ( X, ≤ p ).
Since (C_{k}) is an increasing sequence, (lambda_{k}) is a decreasing sequence.
Thus ({tau_{n}(t)}) is an increasing sequence for all (t>0).
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CEO of Professional Science Editing for Scientists @ prosciediting.com