  It is shown that the Poisson bracket with boundary terms recently proposed by
Bering (hep-th/9806249) can be deduced from the Poisson bracket proposed by the
present author (hep-th/9305133) if one omits terms free of Euler-Lagrange
derivatives ("annihilation principle"). This corresponds to another definition
of the formal product of distributions (or, saying it in other words, to
another definition of the pairing between 1-forms and 1-vectors in the formal
variational calculus). We extend the formula (initially suggested by Bering
only for the ultralocal case with constant coefficients) onto the general
non-ultralocal brackets with coefficients depending on fields and their spatial
derivatives. The lack of invariance under changes of dependent variables (field
redefinitions) seems a drawback of this proposal.
