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The areas aren't non-measurable, that's part of the point. Doing it with non-measurable pieces was already known.
by Sniffnoy 5y ago
The areas aren't non-measurable, that's part of the point. Doing it with non-measurable pieces was already known.
- jessriedel 5y agoThe Quanta article says that doing it non-constructively with non-measurable pieces was already known, and that later results did it partially and then fully constructively (without leaving a measure-zero set). But it does not say in the Quanta article whether or not the pieces in these later results were individually measurable. (The union of non-measurable sets can be measurable.) Are you saying that you know they are?
- Sniffnoy 5y agoWell, when I wrote that I was just inferring it from the article, which while it doesn't explicitly say that they are, is written in a way so as to clearly suggest that they are. But you're right that it doesn't eplicitly say that, now that I look again. But if you click on the link to the actual paper, it says right in the abstract that they're Borel, so yes, they are indeed measurable.
- jessriedel 5y agoThanks!