I'm trying to understand Borel sets. I am looking for a visual (i.e., constructive) $F_{\sigma\delta}$ subset of $[0,1]$ of measure $1$ which is not $F_\sigma$. Any idea or suggestion would be appreciated.
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Use $[0,1]\setminus\Bbb Q$: it’s clearly a $G_\delta$ and therefore an $F_{\sigma\delta}$, but it’s not an $F_\sigma$.
Brian M. Scott
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@pin2: You’re welcome. (I don’t think that you can delete it now that there’s an upvoted answer.) – Brian M. Scott Sep 13 '13 at 11:54
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its ok. Thank you. +1 – pin2 Sep 13 '13 at 11:58
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Didn't you mean in fact: "Not $G_{\delta\sigma}$? – Etienne Sep 13 '13 at 13:23
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@Etienne: No, I meant what I wrote. – Brian M. Scott Sep 13 '13 at 14:07
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In think, the question was for pin2... – Etienne Sep 13 '13 at 18:43