04a - Modern Analysis 2 Test 4 Answer TWO questions 1 Let f...

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Unformatted text preview: Modern Analysis 2 Test 4 Answer TWO questions. 1. Let f ∈ L(µ) and define φ : M → R by A ∈ M ⇒ φ(A) = f dµ. A Show that if ε > 0 is given then there exists δ > 0 such that µ(A) < δ ⇒ |φ(A)| < ε. 2. Let f : R → R be Lebesgue integrable. For t ∈ R define t f F (t) = 0 with respect to Lebesgue measure. Prove that F is continuous. 3. Show that if a ∈ R then ∞ 2 /2 e−t cos(at)dt = 0 1 2 /2 π /2 e−a . ...
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This note was uploaded on 07/08/2011 for the course MAA 5229 taught by Professor Robinson during the Spring '11 term at University of Florida.

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