Does there exists a set which has the exterior measure,but doesn't Lebesgue measurable? Can one give a example of this ? I do really puzzled.
2026-03-25 03:03:12.1774407792
Does there exists a set which has the exterior measure,but doesn't Lebesgue measurable?
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Every set in $\mathbb R^n$ has an exterior measure (sometimes called outer measure). So every subset that is not Lebesgue measurable would be an such an example which you are looking for.
Note that the existence of sets that are not Lebesgue measurable is not constructive. Searching for "Vitali sets" will give more information about this.