Unformatted text preview: ∈ E i } for each x in X . (ii) Show that 1 c : = { ( x 1 , x 2 ) ∈ X 2 : x 1 6= x 2 } = ∪ i ∈ N E i × E c i ∈ A ⊗ A . (iii) Let (Ä, F , P ) be a probability space. Suppose X : Ä → X is an F \ Ameasurable map with distribution P . Suppose X is independent of itself. Show that there exists some x ∈ X for which X = x almost surely [ P ]. Hint: What do you know about P ⊗ P 1 c ?...
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 Spring '09
 DavidPollard
 Statistics, Probability, Probability theory, Suppose Ei, Deﬁne E1

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