Timeline for Is there a maximum to the amount of disjoint non-measurable subsets of the unit interval with full outer measure?
Current License: CC BY-SA 3.0
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| Jan 26, 2014 at 14:58 | comment | added | Andreas Blass | I assume that by "Vitali set" you mean a set that contains exactly one member from each coset of the reals mod the rationals. It's not difficult to obtain such a set with full outer measure. Use the usual transfinite-induction construction of a Bernstein set, but make all choices from different cosets mod the rationals. (At the end, if you haven't got elements from all cosets, throw in additional elements, which can only increase the outer measure.) | |
| Jan 23, 2013 at 15:01 | comment | added | Carlo Mantegazza | Yes I got it. I wrote this before Ramiro posted the reference to the very nice result of Cichon. Anyway, I am now wondering how to construct a Vitali set with full outer measure in R. | |
| Jan 23, 2013 at 14:46 | comment | added | Gerald Edgar | The Vitali construction will give you $\aleph_0$ disjoint sets of full outer measure. But (as we now know) this would not be the best result. | |
| Jan 23, 2013 at 12:19 | history | answered | Carlo Mantegazza | CC BY-SA 3.0 |