Due February 23
- For any two Cantor sets , as constructed in HW2, Problem 3, there exists a continuous, bijective and increasing function that maps surjectively onto .
- There exists a measurable function f and a continous function such that is non-measurable.
Given a collection of sets , there exists a disjoint collection , , such that and each
Problem 3 (Tchebychev inequality)
Let be integrable, and . Then
Let be finite almost everywhere, and . Then f is integrable if and only if
Let and on . Then f is integrable if and only if , and g is integrable if and only if .