[see also: provide, offer, supply, furnish, afford, define, yield, imply, present, produce]
The action of $G$ is given by $gf=$ ......
The argument just given shows that ......
This gives (1) and shows that ......
However, a slight strengthening of the hypotheses does give us a regular measure.
We now give some applications of Theorem 3.
We give $X$ the topology of uniform convergence on compact subsets of $I$.
Note that $E$ can be given a complex structure by setting ......
Suppose we are given an $f$ of the form $f=$ ......
Given $\delta >0$, we can find $\varepsilon$ such that ......
This is certainly reasonable for Algorithm 3, given its simple loop structure.
He used a new version of an algorithm for finding all normal subgroups of up to a given index in a finitely presented group.
A function given on $G$ gives rise to an invariant function on $G'$.
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