Note that $T(g)$ depends on $g$ only through its differential $dg$.
Then $T$ tends to zero only through positive values.
Most distribution spaces can be characterized through the action of appropriate convolution operators.
Through an appeal to (5.3) we have ......
Having established (1), one might be tempted to try to extend this result to general $p$ through the choice of a suitable ideal $B$.
Exercises 2 to 5 [= Exercises 2--5; amer. Exercises 2 through 5]
We now go through the clauses of Definition 3.
On dividing through by $f$, we see that ......
The rest of the proof goes through as for Corollary 2, with hardly any changes.
There are kneading sequences for which the arguments of Section 4 go through routinely.
Multiplying through by $f$ and integrating shows that ......
This assumption enables us to push through the same arguments.
As $t$ runs from 0 to 1, the point $f(t)$ runs through the interval $[a,b]$.
rotation through $\pi/3$ $\langle$through an angle $\theta\rangle$
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