Talk:Littlewood's three principles of real analysis

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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

The comment(s) below were originally left at Talk:Littlewood's three principles of real analysis/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

== Add heuristic examples == The article needs more examples of how the three principles guide us in devising proofs. At present we have only one example. Also please cite any textbooks that give such examples. --Uncia (talk) 20:38, 15 July 2008 (UTC)

Last edited at 20:38, 15 July 2008 (UTC). Substituted at 02:17, 5 May 2016 (UTC)