Timeline for The Weak Besicovitch Covering Property and the Lebesgue Differentation Property
Current License: CC BY-SA 4.0
33 events
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| Sep 2, 2023 at 0:17 | history | edited | M W | CC BY-SA 4.0 |
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| Sep 1, 2023 at 22:29 | history | edited | M W | CC BY-SA 4.0 |
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| Sep 1, 2023 at 19:19 | history | edited | M W | CC BY-SA 4.0 |
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| Sep 1, 2023 at 18:13 | history | edited | M W | CC BY-SA 4.0 |
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| Sep 1, 2023 at 17:42 | history | edited | M W | CC BY-SA 4.0 |
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| Sep 1, 2023 at 17:27 | comment | added | M W | @Grace53 well, I strongly suspect that what I did is probably the same as what Preiss did, so maybe not exactly original:). Nevertheless, you’re quite welcome, it was my pleasure to help with this, was a fun problem! | |
| Sep 1, 2023 at 17:12 | history | edited | M W | CC BY-SA 4.0 |
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| Sep 1, 2023 at 15:12 | vote | accept | Grace53 | ||
| Sep 1, 2023 at 15:11 | comment | added | Grace53 | @M W I read your proof by using the Zorn's Lemma and everything is clear, you had a great and original idea! I don't know how to thank you! | |
| Sep 1, 2023 at 1:20 | comment | added | M W | Also, for what its worth, I removed all the ordinals from the transfinite recursion argument, so it only requires understanding a), the well-ordering theorem (equivalent to axiom of choice) and b) the principle that when a set is well-ordered you can use it for recursive definitions. But it is still optional now that the Zorn's Lemma alternative is there. | |
| Sep 1, 2023 at 1:11 | history | edited | M W | CC BY-SA 4.0 |
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| Sep 1, 2023 at 1:09 | comment | added | M W | @Grace53 I added a Zorn's Lemma argument. Also made a few things more rigorous regarding centers of balls. | |
| Sep 1, 2023 at 1:05 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 31, 2023 at 14:50 | comment | added | Grace53 | @M W Yes, I'm comfortable with Zorn Lemma. Yes, please, if you can show me how to use It without using ordinals and transfinite induction, It would be great. Assume that X Is separable. I Need only This case. | |
| Aug 31, 2023 at 14:47 | comment | added | M W | @Grace53 I don’t think that countable induction will do it, the problem being we have potentially uncountable family of balls, and we have to use exactly that family, so can’t approximate via separability. However, are you comfortable with Zorn’s Lemma? I might be able to translate this into a Zorn’s Lemma argument at some point if that would clarify things. | |
| Aug 31, 2023 at 12:40 | comment | added | Grace53 | @M W I read your proof but I'm not so much familiar with transfinite induction. Is it possible to give a more simple proof in the case $X$ is separable by using only the classical countable inducton? | |
| Aug 28, 2023 at 17:53 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 24, 2023 at 20:59 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 23, 2023 at 12:03 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 23, 2023 at 11:52 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 23, 2023 at 11:11 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 23, 2023 at 10:54 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 23, 2023 at 9:46 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 23, 2023 at 9:40 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 23, 2023 at 9:32 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 23, 2023 at 4:32 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 23, 2023 at 3:17 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 23, 2023 at 3:02 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 23, 2023 at 2:32 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 23, 2023 at 2:04 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 22, 2023 at 22:37 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 22, 2023 at 22:26 | history | edited | M W | CC BY-SA 4.0 |
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| Aug 22, 2023 at 22:20 | history | answered | M W | CC BY-SA 4.0 |