Yi Ni
May 4th, 2004
Committee: David Gabai(chair), Andrei Okounkov, Elias Stein
Length: one hour and 35 minutes
Special topics: Algebraic Topology, Functional Analysis
Okounkov was 5 minutes late, so Stein asked me some questions about
myself before Okounkov came. I guess he wanted to make me relax.
Dave asked what topic I would like to begin with, I said real analysis.
Real and Functional Analysis (Stein, a few by Okounkov)
Cantor set? What special properties does it have?
- Turns out that he wanted the Hausdorff dimension of Cantor set.
I described the meaning of such a "fractional dimension", but didn't
know the definition of Hausdorff dimension.
What special function is related to this set? How to define it?
What property does it have?
- I said that it is constant almost everywhere, and looks like
an infinite stair. He seemed not satisfied, so he asked the more explicit
Suppose we have an increasing function, whose derivative is 0 everywhere,
must it be constant?
What's the correct version of this theorem?
Definition of absolutely continuous function?
Lipschitz condition? Is it absolutely continuous? What if
|f(x)-f(y)|