[see also: which]
That (2) implies (1) is contained in the proof of Theorem 1 of [4].
Clearly, A∞ weights are sharp weights. That there are no others is the main result of Section 2.
The degree of P equals that of Q.
The continuity of f implies that of g.
The diameter of F is about twice that of G.
It is this point of view which is close to that used in C*-algebras.
Define f(z) to be that y for which......
Where there is a choice of several acceptable forms, that form is selected which......
......, that is,......
The usefulness and interest of this correspondence will of course be enhanced if there is a way of returning from the transforms to the functions, that is to say, if there is an inversion formula.
We now state a result that will be of use later.
A principal ideal is one that is generated by a single element.
Let I be the family of all subalgebras that contain F. [Or: which contain F; you can use either that or which in defining clauses.]
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