Born rule in quantum and classical mechanics

Considerable effort has been devoted to deriving the Born rule [i.e., that ${\mid \psi \left(x\right)\mid }^{2}dx$ is the probability of finding a system, described by $\psi$, between $x$ and $x+dx$] in quantum mechanics. Here we show that the Born rule is not solely quantum mechanical; rather, it arises naturally in the Hilbert-space formulation of classical mechanics as well. These results provide insights into the nature of the Born rule, and impact on its understanding in the framework of quantum mechanics.