Ruziewicz problem
In mathematics, the Ruziewicz problem in measure theory asks whether the usual Lebesgue measure on the n-sphere is characterised, up to proportionality, by its properties of being finitely additive, invariant under rotations, and defined on all Lebesgue measurable sets.
This was answered affirmatively and independently for n ≥ 4 by Grigory Margulis and Dennis Sullivan around 1980, and for n = 2 and 3 by Vladimir Drinfeld. It fails for the circle.
The problem is named after Stanisław Ruziewicz.
