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Karl Hofmann assures me that the domain of \beta^{p,q} is indeed
E^{p,q}_\infty, which is the important point.  As for the word used, it is
unimportant since that approach to spectral sequences seems to have gone
by the boards.

Thanks to Mike Mislove for posing this question to Karl.

And now maybe the moderator can shut down this thread.

Michael