Abstract
The customary proof of this well-known theorem uses the convolution product of functions on G. Our proof, which does not seem to be widely known, is shorter and more elementary, even for the real line, than any that we have seen. All references of the form (a.b) are to be found in [1]. PROOF. Since A is regular, we may suppose that A is compact (11.32) and we may choose an open set UDA such that A(U) ?A(vA)+A(A)=22A(A). Therefore, there exist x, yeA such that vx=y and so v=yx-1eAA-1.
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