- #1
- 1,435
- 186
Q: Construct an open subset E of [0,1] having Lebesgue measure [itex]m(E)=\epsilon[/itex] such that [itex]0<\epsilon<1[/itex] which is dense [0,1].
A: The fat Cantor set. I need help proving it is dense in [0,1]. The usual Ternary expansion argument stuff won't work as the sets used are of length [tex]\frac{\epsilon}{3^k}[/tex] at the kth iteration. Ideas?
The details are in the attached PDF:
A: The fat Cantor set. I need help proving it is dense in [0,1]. The usual Ternary expansion argument stuff won't work as the sets used are of length [tex]\frac{\epsilon}{3^k}[/tex] at the kth iteration. Ideas?
The details are in the attached PDF: