Math 73/103
Measure Theory and Complex Analysis
Last updated November 14, 2017 21:06:47 EST

General Information HW Assignments


Homework Assigments

Assignments Made on:
Monday September 11:
  • Read: Review the Riemann integral: $\mathcal R\int_a^b f(x)\,dx$.
  • HW: Work problems 1, 2 and 3 from the First homework assignment. (The assignment was last modified: 12:42 pm, August 22, 2017).
  • If you want the source for the first homework assignment, it is here. You'll need my personal exam class: dpwexam-new.cls. Let me know if there additional missing macro files.
Update: Wednesday, September 13:
  • Read: We're more or less in the very beginning of Chapter 1 of Rudin.
  • Homework: Now you're ready for problems 4, 5 and 6.
  • Optional: Here's an optional little worksheet on Borel sets. Let me know if you want to talk about it.
Some solutions:
Saturday, September 23:
  • Homework: Here is the second assignment. You should start on problems 1--4.
  • E-Mail: I tried to use canvas to circulate this assignment on Saturday morning. If you didn't see the email, you need to tweak your canvas settings.
  • Here is the LaTeX source for homework #2.
Sunday October 1:
  • Homework #2 You should complete the second homework assignment by Friday. (Really, it should be Wednesday, but I forgot to say so earlier.)
  • Not to be turned in: Let $f\in \mathcal{L}^1(X)$ and define $\nu: \mathcal{M}\to \mathbf{C}$ by $$\nu(E)=\int_E f(x)\,d\mu(x).$$ Show that $\nu$ is a complex measure on $(X\mathcal M)$. Show directly (without invoking Hahn/Jordan decompositions) that there are finite (positive) measures $\mu_i$ such that $$\nu(E)= \mu_1(E) -\mu_2(E) +i \bigl(\mu_3(E) - \mu_4(E)\bigr)$$ with $\mu_1\perp \mu_2$ and $\mu_3\perp \mu_4$.
Some Date in early October:
  • Homework: Here is the third assignment. I'm a bit late with this, so all problems are in play. I don't think that the source will be available this time.
Monday, October 16th:
  • Homework: Here is the fourth assignment. You should start on problems 2--8 right away. This is technically "backgroud material", but it will be new to some of you. It is certainly good background for the written quals.
October 21:
  • Homework: Here are some solutions for the third assignment.
Monday, October 30:
  • Last Homework fifth homework. Some of the Rudin problems are trickly. Feel free to ask questions!
November 1:
  • Homework: Here are some solutions for the fourth assignment.
Tuesday 14 November:
  • FINAL EXAM final exam. Sorry for the delay in posting!

Dana P. Williams
Last updated November 14, 2017 21:06:47 EST