# Find some extraordinary subset of [0,1]

## Homework Statement

I want to find a subset A of [0,1] such that A=cl(int A) and bd A does not have measure zero where cl means closure and int means interior.

## The Attempt at a Solution

I tried some sets, but failed.

## Answers and Replies

I tried that set but it was difficult for me to modify it. Can you give me more hint?

Well, you want the fat Cantor set to be the boundary of the set you want.

Every step you leave out some open intervals. Now let V be the union of the open intervals you leave out at the odd steps. Take $\overline{V}$ to be your set.

I think bd of V is not the fat Cantor set..... what should I do?

ah instead of bd of V, boundary of closure of V.