For a locally compact topological group G there exists a non-trivial measure μ‎ on the Borel sets such that

• μ‎ is invariant meaning μ‎(gS) = μ‎(S) for a Borel set S and g ∈ G.

• μ‎ is countably additive meaning $\mu \left({\bigcup }_1^{\infty }{S}_k\right)=\sum _1^{\infty }\mu \left(S_k\right)$ for disjoint S_k.

• μ‎(S) is finite for any compact Borel set S.

• μ‎ is unique up to a multiplication by a positive scalar.