[see also: call for, entail, demand, want, desire, necessitate, force, involve, requisite]
Then $f=1$, as required $\langle$claimed/desired$\rangle$.
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 $I_A(f)$ instead of $I(f)$. [Note that the it is necessary here.]
The above definition was first given in [D]; care is required because this term has been used in a slightly different sense elsewhere.
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 $z_i$ for which we know the structure of $f(z_i)$.
This requires us to give $M$ an $R$-module structure.
We shall show that $V$ is the required open cover.
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