and

 Iml(jXjj) E(JXIu jd BIu).


 2) If, in addition, Bx is separably valued for every x E E and

 if X is u, -integrable, thnthe integral E( X udB ) is defined, and

 2 u
 m(X) E(f XudBu).


 3) The measure m has values in L(E,F) in each of the following

 cases:

 a) F Z'.
 2
 b) For every x c E and v c R, the convex equilibrated

 (balanced) cover of the set B3 (w)x: w C n1 is

 relatively o(F,Z)-compact in F.

 c) For every x E E and v R2, the function 3 x is F-
 +' v
 measurable and almost separably valued; in particular,

 this is the case if F is separable.

Proof. Let p1BI be the measure generated by jBI via Theorem 4.1.4.

For every x E E and z E Z the variation of the process <Bx,z>

satisfies [<Bx,z>I 5 Bl x lzl (cf. proof of Prop. 4.1.3).

Let mz be the stochastic measure generated by <Bx,z>:

m z(M) = E( R21Md<Bx,z>) for M e M. The mapping (x,z) m (M)


is linear in each argument: in fact, mx1+x2,(M) =


E(f 21Md<B(xl+x2),z>) = E( 1Md<Bx +Bx2,z>) = E(f Md(<Bx ,z>+<Bx2,z>))
 H