On the uniqueness of generating Hamiltonian for continuous limits of   Hamiltonians flows
  We show that if a sequence of Hamiltonian flows has a $C^0$ limit, and if the generating Hamiltonians of the sequence have a limit, then this limit is uniquely determned by the limiting $C^0$ flow. This answers a question by Y.G. Oh. 
Claude Viterbo (CMLS-X)