Talk:Lebesgue differentiation theorem

"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.

140.180.4.116 (talk) 13:53, 14 May 2008 (UTC)

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)

oops. Already there. Silly me. RayAYang (talk) 16:15, 3 December 2008 (UTC)

The definition of bounded eccentricity isn't right 2601:84:8101:34B0:B4EF:D55F:EFA3:4340 (talk) 01:42, 21 October 2024 (UTC)