  Recently, the present authors studied perturbations in the
Lemaitre-Tolman-Bondi cosmological model by applying the second-order
perturbation theory in the dust Friedmann-Lemaitre-Robertson-Walker universe
model. Before this work, the same subject was studied in some papers by
analyzing linear perturbations in the Lemaitre-Tolman-Bondi cosmological model
under the assumption proposed by Clarkson, Clifton and February, in which two
of perturbation variables are negligible. However, it is a non-trivial issue in
what situation the Clarkson-Clifton-February assumption is valid. In this
paper, we investigate differences between these two approaches. It is shown
that, in general, these two approaches are not compatible with each other. That
is, in our perturbative procedure, the Clarkson-Clifton-February assumption is
not valid at the order of our interest.
