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"The theorem also holds if cubes are replaced by arbitrary sets with diameter tending to zero, in the definition of the derivative."
I find this sentence confusing, and recommend its removal for two reasons:
(1) The theorem is stated with balls.
(2) I think it is false e.g. for thin rectangles pointing in arbitrary directions. See Chap. II and X in E. M. Stein, Harmonic Analysis.
Ah. It's true for sets of bounded eccentricity. So not arbitrary sets, but ... I'll see if I can find a way to work it in. RayAYang (talk) 22:43, 2 December 2008 (UTC)Reply
