  Evans (1992) described the semi-group of a superprocess with quadratic
branching mechanism under a martingale change of measure in terms of the
semi-group of an immortal particle and the semigroup of the superprocess prior
to the change of measure. This result, commonly referred to as the spine
decomposition, alludes to a pathwise decomposition in which independent copies
of the original process `immigrate' along the path of the immortal particle.
For branching particle diffusions the analogue of this decomposition has
already been demonstrated in the pathwise sense, see for example Hardy and
Harris (2009). The purpose of this short note is to exemplify a new {\it
pathwise} spine decomposition for supercritical super-Brownian motion with
general branching mechanism (cf. Kyprianou et al. (2010)) by studying $L^p$
convergence of naturally underlying additive martingales in the spirit of
analogous arguments for branching particle diffusions due to Hardys and Harris
(2009). Amongst other ingredients, the Dynkin-Kuznetsov $\mathbb{N}$-measure
plays a pivotal role in the analysis.
