2654 CHAPTER 77. STOCHASTIC INCLUSIONS

for each ω, one obtains the convergences 77.8.91 - 77.8.96 as n → ∞. As before, foreach ω,z(·,ω) ∈ Ã(w(·,ω) ,ω) a.e. where t → w(t,ω) is the function to which wn (·,ω)converges weakly. Note that the estimates allowing this to happen are dependent on ω .However, one can apply Theorem 77.2.10 as before and obtain a solution to

Bw(t,ω)+∫ t

0z(s,ω)ds+

∫ t

0g(s,ω)ds =

∫ t

0f (s,ω)ds+Bu0 (ω)

such that w,z,g are product measurable into V or V ′ and ,z(·,ω) ∈ Ã(w(·,ω) ,ω). Now letu(t,ω) = w(t,ω)+q(t,ω) to obtain the existence of the desired solution in the corollary.