Talk:Littlewood's three principles of real analysis

Untitled
It is not actually an 'obvious' result that if the functions converged uniformly, we could exchange the limits. We need a bounded domain of integration as well for that. Maybe we should change that. — Preceding unsigned comment added by 124.168.61.100 (talk) 15:44, 11 September 2011 (UTC)

Agreed, neither obvious nor true, therefore changed. Rfs2 (talk) 12:53, 31 May 2012 (UTC)

(Older comments)
Maybe we should use "nearly" instead of "almost" in the statements of the principles. In measure theory, "almost" usually means "except for a zero set", while here it is "except for a $$\epsilon$$ set", so "nearly" may be a better choice.

I think in Royden's book, he used "nearly" rather than "almost".

74.12.80.128 05:51, 7 April 2007 (UTC)

I believe there is a slightly stronger statement for the first principle. It says:

Any measurable set of finite measure is nearly a FINITE union of open INTERVALS. Yongfei Ci 22:52, 19 August 2007 (UTC)

Assessment comment
Substituted at 02:17, 5 May 2016 (UTC)