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Miscellany2 - μ n A 3 Let Ω F μ be a finite measure...

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Analysis 2 Miscellaneous Problems 2 1. Let C be a collection of subsets of the set Ω . For each A σ ( C ) show that there is a countable subcollection C A of C such that A σ ( C A ). 2. Let ( Ω , F ) be a measurable space on which ( μ n : n N ) is an increasing sequence of measures. Show that a measure μ on ( Ω , F ) is defined by the rule A ∈ F ⇒ μ ( A ) = lim
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Unformatted text preview: μ n ( A ) . 3. Let ( Ω , F , μ ) be a finite measure space; for convenience, let ∅ be the only null set. Show that the rule A , B ∈ F ⇒ d ( A , B ) = μ ( A 4 B ) defines a metric d on F . Verify that the operations of union and intersection are uniformly continuous. 1...
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