Someone please explain this: Presume that for each $x \in \mathbb{R}$ and $A \subseteq \mathbb{R}$, that $x + A = \big\{ x + a \mid a \in A \big\}$. Here, A and x + A are Borel sets for all $x \in \mathbb{R}$.
Then, if $\mu$ is a σ-finite measure on B (so that λ($\mathbb{R}$) = ∞) and λ is a translation invariant, how can it be shown that there exists a real number c > 0 such that $\mu$ = c λ? I know that $\mu$(A) = c λ(A) for all Borel sets A. I also know that the Lebesgue measure is the unique translation invariant measure on B, up to a multiplicative constant.