High Quality Content by WIKIPEDIA articles! In mathematics, the Ruziewicz problem (sometimes Banach-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 by Vladimir Drinfel'd (published 1984) for n = 2 and 3, and for n ? 4 by Grigory Margulis and Dennis Sullivan around 1980. It fails for the circle. The name is for Stanis?aw Ruziewicz.

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