Ergodic Theory and Dynamical Systems

Research Article

Finitely-additive invariant measures on Euclidean spaces

G. A. Margulis

Abstract

It is shown that for n ≥ 3 the Lebesgue measure is the unique finitely-additive isometry-invariant measure on the ring of bounded Lebesgue measurable subsets of the n-dimensional Euclidean space.

(Received August 10 1981)