  We outline a statistical theory of turbulence based on the Lagrangian
formulation of fluid motion. We derive a hierarchy of evolution equations for
Lagrangian N-point probability distributions as well as a functional equation
for a suitably defined probability functional which is the analog of Hopf's
functional equation. Furthermore, we adress the derivation of a generalized
Fokker-Plank equation for the joint velocity - position probability density of
N fluid particles.
