[see also: call for, entail, demand, want, desire, necessitate, force, involve
Then f=1, as required <claimed/desired>.
In addition to f being convex, we require that F be holomorphic. [Note the subjunctive be.]
This is equivalent to requiring that......
If (ii) is required for finite unions only, then M is called an algebra of sets.
When clarity requires it, we shall write IA(f) instead of I(f). [Note that the it is necessary here.]
Many of the results that follow only require W to satisfy (8).
The algebraic properties (i) and (ii) required of j are evidently true.
Lemma 3 does not require D to be prime.
The only point that requires care is the verification of......
The projection technique requires the introduction of an appropriate homomorphism.
We require a method of dividing z into subwords zi for which we know the structure of f(zi).
We shall show that V is the required open cover.