Difference between revisions of "Talk:F-sigma"
From Encyclopedia of Mathematics
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: 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.[[User:Camillo.delellis|Camillo]] 14:15, 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.[[User:Camillo.delellis|Camillo]] 14:15, 16 August 2012 (CEST) | ||
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| + | : 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. [[User:Camillo.delellis|Camillo]] 15:29, 16 August 2012 (CEST) | ||
Revision as of 13:29, 16 August 2012
"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)
How to Cite This Entry:
F-sigma. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=F-sigma&oldid=27597
F-sigma. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=F-sigma&oldid=27597