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## 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.

## Homework Equations

## The Attempt at a Solution

I tried some sets, but failed.

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- Thread starter Maclaurin
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- #1

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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.

I tried some sets, but failed.

- #2

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Try to do something with that. You may have to modify it.

- #3

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

- #4

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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 [itex]\overline{V}[/itex] to be your set.

- #5

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

- #6

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

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