  In 2017, Lienert and Tumulka proved Born's rule on arbitrary Cauchy surfaces
in Minkowski space-time assuming Born's rule and a corresponding collapse rule
on horizontal surfaces relative to a fixed Lorentz frame, as well as a given
unitary time evolution between any two Cauchy surfaces. Here, we prove Born's
rule on arbitrary Cauchy surfaces from a different, but equally reasonable, set
of assumptions. The conclusion is that if detectors are placed along any Cauchy
surface $\Sigma$, then the observed particle configuration on $\Sigma$ has
distribution $|\Psi_\Sigma|^2$, suitably understood. The main different
assumption is that the Born and collapse rules hold on any spacelike
hyperplane, i.e., at any time coordinate in any Lorentz frame. Heuristically,
this follows if the dynamics of the detectors is Lorentz invariant. In
addition, we assume, as did Lienert and Tumulka, that there is no interaction
faster than light and that there is no propagation faster than light.
