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Show that any set of the form
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is a Borel set. That is, the product of Borel sets is Borel. Hint: You might consider the continuous functions πi : ∏ j=1nXj → Xi which are the projection maps. Thus πi
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Explain why this function is continuous, equals 0 off V and equals 1 on K.
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Show that if this happens, then there exists a set of measure N such that if ω
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Also show that limn→∞fn