Notional particles initial distribution

It is important to recognize that (6.164) is a direct result of choosing the uniformly distributed initial locations (6.163). In contrast, if one chooses to start all notional particles at the origin /V(y) = <5(y), then /x (x t) will be non-uniform, and the Lagrangian notional-particle PDF will not correspond to the Lagrangian fluid-particle PDF. 

If the initial particle locations are uniformly distributed and (6.160) holds, then (6.167) relates the Eulerian notional-particle PDF to the Eulerian PDF (for fixed x and t with... 

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