  In this paper we partially answer a question of P. Tukia about the size of
the difference between the big horospheric limit set and the horospheric limit
set of a Kleinian group. We mainly investigate the case of normal subgroups of
Kleinian groups of divergence type and show that this difference is of zero
conformal measure by using another result obtained here: the Myrberg limit set
of a non-elementary Kleinian group is contained in the horospheric limit set of
any non-trivial normal subgroup.
