  We investigate the position- and momentum-space two--body correlations in a
weakly interacting, harmonically trapped atomic Bose-Einstein condensed gas at
low temperatures. The two-body correlations are computed within the Bogoliubov
approximation and the peculiarities of the trapped gas are highlighted in
contrast to the spatially homogeneous case. In the position space, we recover
the anti-bunching induced by the repulsive inter-atomic interaction in the
condensed fraction localized around the trap center and the bunching in the
outer thermal cloud. In the momentum space, bunching signatures appear for
either equal or opposite values of the momentum and display peculiar features
as a function of the momentum and the temperature. In analogy to the optical
Hanbury Brown and Twiss effect, the amplitude of the bunching signal at
close-by momenta is fixed by the chaotic nature of the matter field state and
its linewidth is shown to be set by the (inverse of the) finite spatial size of
the associated in-trap momentum components. In contrast, the linewidth of the
bunching signal at opposite-momenta is only determined by the condensate size.
