1 авг. 2018 г. · The sets Vk are disjoint and countable, hence the measure of the union is exactly equal to the sum of measures.

23 авг. 2017 г. · No measure on the Vitali set can meet the conditions that a measure should: correspond to length for intervals; be countably additive; be monotone; be ...

1 дек. 2018 г. · The construction of the Vitali set shows it cannot be a member of any sigma algebra that has a nontrivial translation-invariant measure. If our ...

28 апр. 2012 г. · If we do that in the interval [0,1] instead of all R, this set A is called Vitali set and we can show that it cannot be measurable.

2 янв. 2022 г. · A Vitali set is not Lebesgue measurable. But I'm not sure how anyone could come up with that out of thin air.

3 сент. 2015 г. · A Vitali set is non-measurable, direct proof, without using countable additivity · It's a shame you picked Vitali sets and outer measures for ...

19 июл. 2015 г. · Since the Vitali set is non-measurable, there must exist some set A that does not satisfy the equation.

23 дек. 2022 г. · Given a Vitali set V⊂[0,1] and a positive measure set A⊆[0,1], prove that their intersection is not measurable.

11 апр. 2023 г. · It is possible to have a Vitali set V⊂[0,1] such that V+V contains all of (0,2) and thus is measurable.

1 окт. 2021 г. · We know that any set with zero outer measure is measurable, and the vitali set on [0,1] is non-measurable. So it must have a non-zero outer ...