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Advanced Analysis Chapter 7: Content and Measure Questions with Complete Solutions
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Def: Boolean Algebra Correct Answer-A Boolean algebra on a set X is a ℬ ∈ ℘(℘(X)) s.t. - ∅ ∈ ℬ - E ∈ ℬ ⇒ X E ∈ ℬ - E, F ∈ ℬ ⇒ E ∪ F ∈ ℬ. Examples of Boolean Algebras Correct Answer-- The trivial boolean algebra on X is {X,∅} - The discrete algebra on X is ℘(X). - The set ℬ of finite unions of intervals is a boolean algebra on ℝ Def: Interval Correct Answer-We attempt to define intervals as one class instead of a list of possible types: I ∈ ℘(R) is said to be an interval if: (x, z ∈ I) ∧ (x ≤ y ≤ z) ⇒ y ∈ I Prop 7.1.9: Smallest Boolean Algebra Correct Answer-Suppose
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advanced analysis chapter 7 content and measure q
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