I am looking for a proof/reference of the following theorem in measure theory:
Every isometry-invariant Radon measure $\mu$ on $[\mathbb{R}^d, \mathcal{B}^d]$ is a constant multiple of the Lebesgue measure, means $\mu = c \lambda$ for a constant $c\geq 0$.
I found this statement in "Stochastic Geometry and its Application" by Stoyan, Kendall, and Mecke, but there was neither a proof nor a reference.
If you know about a reference, please let me know.