mid1 - Write your name clearly on all sheets of paper you...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Write your name clearly on all sheets of paper you will turn in and possibly number them. Write clearly and large enough to be easily readable. Your poofs must be complete and clearly written. Each question is worth the number of points indicated. Fifty ±ve points will grant you an A but you have to solve at least one between ex. 1 and ex. 2. 1 (15 pts) Let f : R R 2 be a C 1 function ( i.e. f is continuous, di²erentiable and the derivative is continuous). Prove that μ ( f ( R )) = 0, where μ is the Lebesgue measure on R 2 . 2 Let M 1 and M 2 be two σ -algebras of subsets of X . Let μ 1 be a measure de±ned on M 1 and μ 2 be a measure on M 2 . a) (10 pts) Give a de±nition for the measure μ = μ 1 + μ 2 . On which σ -algebra M is μ de±ned? Show that your de±nition de±nes a measure. b) (10 pts) Show that if μ 1 and μ 2 are complete than μ = μ 1 + μ 2 is complete. c) (10 pts) Show that if μ 1 ± ± M and μ 2 ± ± M are σ -±nite than μ = μ 1 + μ 2 is also σ -±nite. 3 Let (
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/17/2010 for the course STATISTIC 472 taught by Professor Amjad during the Spring '08 term at Yarmouk University.

Page1 / 2

mid1 - Write your name clearly on all sheets of paper you...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online