From Encyclopedia of Mathematics
Revision as of 16:02, 16 August 2012 by Boris Tsirelson (talk | contribs) (terminology)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

"and which is not itself closed"?? In the books I read F is included into Fsigma (and generally, each class is wider than previous classes). --Boris Tsirelson 11:09, 16 August 2012 (CEST)

The one I consulted insists in excluding closed sets (and, consistently, excludes $F_\sigma$ from $F_{\sigma\delta}$ and so on): it is either Cohn or Royden (I don't have it with me at home) and I noticed that it uses this convention for Baire classes as well. What about saying: "some authors exclude closed sets and some authors include them"? In any case I am not so keen on any of the two conventions: if you insist we can just take the one of your books.Camillo 14:15, 16 August 2012 (CEST)
Thinking about it, it seems a better convention not to exclude closed sets. For instance, when proving a theorem like "Any Lebesgue measurable set is the union of an $F-_\sigma$ and a null set" the other convention would create some silly case to discuss. Camillo 15:29, 16 August 2012 (CEST)
I'd say, in such cases we must mention existing terminological distinctions. Sometimes we can avoid taking one side (if the distinction is not so important for the text of the article), sometimes not. --Boris Tsirelson 18:02, 16 August 2012 (CEST)
How to Cite This Entry:
F-sigma. Encyclopedia of Mathematics. URL: