[see also: assertion, statement]
The first conclusion is immediate from Theorem 1.
This conclusion does not follow if the condition “$f\in A$” is omitted.
Part of the conclusion is that $F$ moves each $z$ closer to the origin than it was.
One might hope that in the particular case of the GL energy, this could be established, but we do not see an easy path to such a conclusion.
......, which is the desired conclusion.
Actually, the proof gives an even more precise conclusion: ......
Identical conclusions hold in respect of the condition BN. [= concerning BN]
Here are some other situations in which we can draw conclusions only almost everywhere.
However, a few tentative [= cautious, not firm] conclusions can be drawn.
We shall see that the two cases where $A=1$ and where $B=2$ give contrasting conclusions.
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