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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 . ...
View Full Document

Ask a homework question - tutors are online