- #1
Kreizhn
- 743
- 1
Homework Statement
Construct a sequence [itex] (G_n) [/itex] of dense open subsets of [itex] \mathbb{R} [/itex] such that
[tex] \lambda \left( \bigcap_{n=1}^\infty G_n \right) = 0 [/tex]
and hence deduce that there exists an uncountable subset of [itex] \mathbb{R} [/itex] of measure 0
Homework Equations
[itex] \lambda [/itex] is the Lebesgue measure on [itex] \mathbb{R} [/itex]
The Attempt at a Solution
This really just seems like a pseudo-extension of the Cantor set to [itex] \mathbb{R} [/itex], but I'm not sure how to go about constructing it.