[sth; sth to be sth; sb to do sth; see also: enable, permit, possible]
These theorems allow one to guess the Plancherel formula. [Or: allow us to guess; not: “allow to guess”]
As the space of Example 3 shows, complete regularity of $X$ is not enough to allow us to do that.
This allows proving the representation formula without having to integrate over $X$.
This easily allows the cases $c=1,2,4$ to be solved.
By allowing $f$ to have both positive and negative coefficients, we obtain ......
It is therefore natural to allow (5) to fail when $x$ is not a continuity point of $F$.
The limit always exists (we allow it to take the value $\infty$).
Lebesgue discovered that a satisfactory theory of integration results if the sets $E_i$ are allowed to belong to a larger class of subsets of the line.
In [3] we only allowed weight functions that were $C^1$.
It should be possible to enhance the above theorem further by allowing an arbitrary locally compact group $L$.
Here we allow $a=0$.
We deliberately allow that a given $B$ may reappear in many different branches of the tree.
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