Question: 5.3. Let L2 {Y : E(|Y |2) < }. For Yn,Wn L2, define < Yn,Wn > E(YnWn), and write Y = l.i.m.nYn and

5.3. Let L2 ≡ {Y : E(|Y |2) < ∞}. For Yn,Wn ∈ L2, define < Yn,Wn >≡

E(YnWn), and write Y = l.i.m.n→∞Yn and W = l.i.m.n→∞Wn. Then, show that

< Y,W >= lim n→∞ < Yn,Wn >, (continuity of inner product).

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