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jem05
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Homework Statement
Let V a subset of the real line be called a vitali set if V contains precisely one point from each coset of the group of rational numbers. Prove:
Homework Equations
1) every lebesgue measurable subset of V is a nullset.
2) V is not lebesgue measurable
3) every set of positive Lebesgue outer measure contains a set that is not lebesgue measurable.
The Attempt at a Solution
i already did 1 and 2.
i am stuck at 3,
i think i need to consruct a vitali set in the given one which i could do if the set contains an interval,..
but it doesn't need to , all i could know about it is that it is not countable since if it were, then its outermeasure will be zero.
thanks a lot
any help is appreciated