Final Exam, Math 245C, June 4, 2007. Exams are due June 13 at 6:00 PM in my mailbox. You may use your course notes or any book available, including Folland and Hrmander, but you should write out a o c
1
9. S IGNED MEASURES AND THE R ADON -N IKODYM THEOREM
The purpose of this section is to prove the Radon-Nikodym theorem and discuss generally the
subject of absolutely continuous and singular measure
Math 245A, Real Analysis
Fall 2015
Final
Name:
There are five problems with a total of 50 points.
Problem 1: Let (X, A) be a measurable space and fn : X C for n N be
measurable functions. Consider the
245C notes, Spring 2015
Shyr-Shea Chang
4/1
Regular meeting on 9 am on Thursdays.
Interpolation
Thm. (Riesz-Thorin) Let (X, F, ) be -finite measure space, Lp be the
R
1
space of measurable f : X C wit