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
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.
 Spring '11
 Robinson

Click to edit the document details