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(C) (i) For every, is -measurable in ; (ii) For -a.e.,.

Therefore, for every, is a nondecreasing sequence of numbers in.

A -semigroup is called differentiable for if for every, is differentiable for.

If for every, is nonnegative and is nonnegative, then the solution,, to (2.10) is nonnegative.

Let be normed space with norm Then the functions defined by and for every, are -distance.

So we may assume that for every, is odd and is even.

Then the delay difference (1.1) is equivalent to (1.13) if for every is defined by (4.21).

(AR) For every, is continuously differentiable in, and there is a constant  such that (1.5).

there exist,, and, such that ;, where ; for every, is a relatively compact set of, where (2.2).

for every ; are positive bounded linear functionals on given by (2.23).

Then, if for every, is a weak solution to and (2.8).

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