By the Riesz representation for linear functionals, f is a bounded linear
functional on [B] if and only if there is a unique element 
,
for which
The difference between the prior expectation 
and the observed adjusted
expectation 
defines a linear functional
on [B]. Therefore by the Riesz representation, if 
is bounded on
[B]
, then there is a unique element 
,
corresponding to , for which
This element is precisely the bearing as created in section 4,
and the properties of the bearing may be deduced directly from this
representation. Note that in the preceding sections we have also used the Riesz
representation to create the bearing for two other functionals, namely the difference functional,
, and also the functional which replaces each
X by its observed value.