Miscellany2 - n ( A ) . 3. Let ( , F , ) be a nite 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: n ( A ) . 3. Let ( , F , ) be a nite measure space; for convenience, let be the only null set. Show that the rule A , B F d ( A , B ) = ( A 4 B ) denes a metric d on F . Verify that the operations of union and intersection are uniformly continuous. 1...
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This note was uploaded on 07/08/2011 for the course MHF 3202 taught by Professor Larson during the Spring '09 term at University of Florida.

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