Due June 1
- Let satisfy a Hölder condition of exponent . Then f is constant.
- Is is a surjective Hölder function of exponent , then . (Prove directly, without using Lemma 2.2 from the text.)
Let be the set
Then and .
Let be an odd integer and consider the “middle th” set K, that is, the result of the Cantor process when removing the middle interval of length of the previous interval.
- Prove that for any , there exists a totally disconnected perfect set in whose dimension is larger then .
There exists a Cantor-like set that has Lebesgue measure zero and Hausdorff measure 1.