# Talk:F-sigma

From Encyclopedia of Mathematics

"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: http://encyclopediaofmath.org/index.php?title=F-sigma&oldid=27605