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Miscellany5 - Analysis 2 Miscellaneous Problems 5 1 Let F...

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Analysis 2 Miscellaneous Problems 5 1. Let ( Ω , F , μ ) be an arbitrary measure space and let 1 6 p < q < . Show that if p < t < q then L p ( Ω , F , μ ) ∩ L q ( Ω , F , μ ) ⊆ L t ( Ω , F , μ ). 2. Let Ω be an uncountable set and F be its σ -algebra of countable or cocountable subsets. On ( Ω , F ), let μ be counting measure and let ν be the measure taking value 0 on countable sets and 1 on uncountable sets. Show that
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