hw4 - R by f ( x ) = μ ( V + x ) . Is f necessary...

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Math 240A: Real Analysis, Fall 2011 Homework Assignment 4 Due Friday, October 21, 2011 1. The Dirac measure δ concentrated on { 0 } is a Borel measure on R . Find all the increasing and right-continuous functions F : R R such that μ F = δ. 2. Let μ be a ±nite Borel measure on R . Let V be a nonempty, bounded, open subset of R . For any x R de±ne V + x = { v + x : v V } . De±ne f : R
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Unformatted text preview: R by f ( x ) = μ ( V + x ) . Is f necessary continuous? 3. Exercise 26 on page 39. 4. Exercise 29 on page 39. 5. Exercise 33 on page 40. 6. Exercise 3 on page 48. 7. Exercise 4 on page 48. 8. Let 0 < α < 1 . Construct an open set E ⊂ [0 , 1] so that E is dense in [0 , 1] and m ( E ) = α....
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This note was uploaded on 12/11/2011 for the course MATH 240a taught by Professor Rothschild,l during the Fall '08 term at UCSD.

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