  We construct a quasi-local formalism for conserved charges in a theory of
gravity in the presence of matter fields which may have slow falloff behaviors
at the asymptotic infinity. This construction depends only on equations of
motion and so it is irrespective of ambiguities in the total derivatives of the
Lagrangian. By using identically conserved currents, we show that this
formalism leads to the same expressions of conserved charges as those in the
covariant phase space approach. At the boundary of the asymptotic AdS space, we
also introduce an identically conserved boundary current which has the same
structure as the bulk current and then show that this boundary current gives us
the holographic conserved charges identical with those from the boundary stress
tensor method. In our quasi-local formalism we present a general proof that
conserved charges from the bulk potential are identical with those from the
boundary current. Our results can be regarded as the extension of the existing
results on the equivalence of conserved charges by the covariant phase space
approach and by the boundary stress tensor method.
