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: dpwexamnew.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 14.
 EMail: 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 28 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!
