Note that O(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.
Exercises 2 to 5 [= Exercises 2--5; amer.: Exercises 2 through 5]
The rest of the proof goes through as for Corollary 2, with hardly any changes.
On dividing through by f, we see that......
Multiplying through by f and integrating shows that......
As t runs from 0 to 1, the point f(t) runs through the interval [a,b].
rotation through π/3 <through an angle θ>
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