Sheet2 - (2.4) Suppose T : X → Y and that A is a...

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

View Full Document Right Arrow Icon
Statistics 330/600 Due: Thursday 27 January 2005: Sheet 2 Please attempt at least the starred problems. *(2.1) (H¨older inequality) UGMTP Problem 2.15 or 2.16, not both. Be careful with log 0. *(2.2) (Minkowski inequality/Orlicz norm) UGMTP Problem 2.17 or 2.22, not both. If you do 2.22, deduce the Minkowski inequality as a special case. *(2.3) (completeness of L 1 ) UGMTP Problem 2.18.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (2.4) Suppose T : X → Y and that A is a sigma-Feld of subsets of X . (i) Show that B : = { B ⊆ Y : T − 1 ( B ) ∈ A } is a sigma-Feld on Y . (ii) Show that B is the largest sigma-Feld for which T is A \ B-measurable. (2.5) Verify all the assertions made in the paragraph following DeFnition 2.27 of UGMTP regarding the µ-completion of a sigma-Feld....
View Full Document

This note was uploaded on 11/21/2009 for the course STAT 330 taught by Professor Davidpollard during the Spring '09 term at Yale.

Ask a homework question - tutors are online