62.12. THE SPACE M pT (E) 2113

which converges to 0 due to the definition of M pT (E) which requires that

supt∈[0,T ]

||M (t)||p ∈ L1 (Ω,F ,P) .

Since the sets[supt∈[0,T ] ||M (t)|| ≥ λ

]decrease to /0 as λ →∞, the dominated convergence

theorem implies the integral on the right in 62.12.50 converges to 0.