Construction of a small but fat set?

Question

Is it possible to find a subset $A$ of the real line $\mathbb R$ such that the Lebesgue measure of $A$ minus its interior is positive ?

See here for an equivalent, more general question. Note that $\partial A = \overline A \setminus A^\circ$; the frontier is the set minus its interior. — AlexR, Aug 19 '14 at 14:47
@AlexR : Usually, $\partial A=\overline{A}\setminus A^°$, doesn't it ? — Student, Aug 19 '14 at 14:50

score 1 · Answer 1 · answered Aug 19 '14 at 14:47

1

What about $(\Bbb R-\Bbb Q)\cap [0,1]$

answered Aug 19 '14 at 14:47

Hamou

score 1 · Answer 2 · edited Apr 13 '17 at 12:20

1

A fat Cantor set. A is closed, its interior is empty, so $A$ minus its iterior is $A$ itself. See previous question: https://math.stackexchange.com/a/287872/442

edited Apr 13 '17 at 12:20

Community

answered Aug 19 '14 at 14:53

GEdgar

2 Answers2