Is there a compact set with positive measure on $[0,1]\setminus \Bbb Q$
69273
Is there a compact subset of the irrationals with positive Lebesgue measure?
128894
About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
60053
Does the boundary of an open set have measure zero (in $\mathbb{R}^n$)?
69499
Let $A\subset\mathbb{R}$ a measurable and bounded set. Show that exists for each $0\alpha$.
65595
Let $\lambda(A)$ be the Lebesgue measure of $A$. There exists an interval $I$ such that $\lambda(E \cap I) / \lambda(I) < 1-\epsilon$
92005
Existence of compact/complete metric on countable set
80202
Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
6675
Lebesgue measurable set that is not a Borel measurable set
51914
Show that $S$ is compact.
69534
Measure of the Cantor set plus the Cantor set
74720
Is every set of measure zero countable?
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
29303
Cartesian product of compact sets is compact
130066
If $\ \sum_{k=1}^n m(E_n) > n-1,$ then prove that $\bigcap_{k=1}^n E_k$ has positive measure.
19773
Is finite additivity a property of the Lebesegue outer measure?
95294
Dense subset of $C[0,1]$ which preserves rationals
7402
Showing a compact metric space has a countable dense subset