Classical wave functions with ρ = |ψ|² were introduced after Koopman and von Neumann, probably by Schönberg, so calling them 'KvN waves' is a misattribution.
Hidden BRS Invariance in Classical Mechan- ics. II
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The History of Hilbert-Space Formulations of Classical Physics
Classical wave functions with ρ = |ψ|² were introduced after Koopman and von Neumann, probably by Schönberg, so calling them 'KvN waves' is a misattribution.