  The work is devoted to the proof of the conservation of local
field-theoretical Hamiltonian structures in Whitham's method of averaging. The
consideration is based on the procedure of averaging of local Poisson bracket,
proposed by B.A.Dubrovin and S.P.Novikov. Using the Dirac procedure of
restriction of the Poisson bracket on the submanifold in the functional space,
it is shown in the generic case that the Poisson bracket, constructed by method
of Dubrovin and Novikov, satisfies the Jacobi identity. Besides that, the
invariance of this bracket with respect to the choice of the set of local
conservation laws, used in this procedure, is proved.
