This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 5. (a) Let S be a collection of subsets of [0 , 1] that is closed under countable unions. Suppose : S R is a set function satisfying the rst three conditions for being a measure. In addition, suppose is i. nitely additive (meaning ( A ) = n i =1 ( A i ) for A = S n i =1 A i with A i S and A i A j = whenever i 6 = j ); and ii. countably sub-additive (meaning ( A ) i =1 ( A i ) for A = S i =1 A i with A i S and A i A j = whenever i 6 = j ). Prove that is a measure on S . (b) Explain why Exercise 9.29 is an easy corollary of part (a). 1...
View Full Document
This note was uploaded on 08/20/2011 for the course MATH 318 taught by Professor Staff during the Spring '08 term at Haverford.
- Spring '08