Linda Brown Westrick
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 Nov 28 awarded Nice Question Apr 9 accepted Degree of unsolvability of finding a open approximation to a Borel set, given its Borel code Apr 6 comment Degree of unsolvability of finding a open approximation to a Borel set, given its Borel code I'm glad to know of this nice paper of Hinman. As for my question, I'll accept your answer of "folklore" in a few days if no references come up before then. Apr 5 comment Degree of unsolvability of finding a open approximation to a Borel set, given its Borel code (I have a pdf now, thank you MO!) Apr 5 comment Degree of unsolvability of finding a open approximation to a Borel set, given its Borel code Thank you for the reference. I couldn't find an electronic copy in the usual places, so my response will take a little longer. (If anyone has a pdf handy I would be grateful for the share.) Apr 5 comment Degree of unsolvability of finding a open approximation to a Borel set, given its Borel code Liang Yu, thank you for the nice example. It is short and pleasing, but different from what I am looking for in two ways. First, the fact I wish to cite would give the exact degree of unsolvability for each $\alpha$, while this example leaves a few jumps' gap. (The gap can be closed by coding $0^{(\alpha)}$ into the $U$.) Second, I'm looking for a reference, not a proof sketch. When I need to cite folklore, I will generally write up a proof for the sake of the literature's completeness. However, I prefer to hope that someone wrote it already! Apr 4 asked Degree of unsolvability of finding a open approximation to a Borel set, given its Borel code Jul 2 awarded Curious May 2 awarded Nice Question May 1 comment Is this property equivalent to Lusin's property (N) for continuous functions? And what a marvelous book it is, both efficient and clear. I think I'll be buying a Dover copy myself. Thank you Christian! May 1 accepted Is this property equivalent to Lusin's property (N) for continuous functions? Apr 29 asked Is this property equivalent to Lusin's property (N) for continuous functions? Feb 20 comment Reference for the fact that the images of the narrow and wide Denjoy integrals are respectively $ACG_\ast$ and $ACG$? Saks does seem to have this, though it is not set aside as a theorem, at a first look-through I think all the pieces are there. It has a very pleasing parallel analysis of the narrow and wide cases in Chapter VIII, sections 1,4 and 5. Thank you! Feb 20 accepted Reference for the fact that the images of the narrow and wide Denjoy integrals are respectively $ACG_\ast$ and $ACG$? Feb 20 comment Error of midpoint method for functions that are not twice-differentiable I meant with the checkbox, but in any case I'm glad it helped. Feb 19 awarded Yearling Feb 18 comment Error of midpoint method for functions that are not twice-differentiable There are certainly some hypotheses one could add to get rid of the kind of bad behavior above. For a very weak example, I don't know how to make an $O(1/n)$ convergence with an absolutely continuity restriction. If you're satisfied with my answer, though, I hope you will accept it :-) Feb 18 comment Algebraic characterization of real differentiation For example, the polynomials are dense in $C^1[a,b]$ for the topology of uniform convergence (Stone-Weierstrass). But the derivative operator is not continuous with respect to this topology. This example does not contradict your answer, nor does it directly address the OP. But the thing I am confused about is under what circumstances would one be able to use your answer to identify the derivative. Feb 17 comment Algebraic characterization of real differentiation With respect to what topology should the rational functions be dense and the operator continuous? Feb 17 comment Error of midpoint method for functions that are not twice-differentiable Now I think I understand your previous comments -- you are just as interested in the "$o$" as the "$1/n$". I added a nasty function for which the error fails to be $o(1/n)$.