Question about measure zero

1. Oct 29, 2006

ak416

I saw this come up in a proof: Since A is a Jordan measurable set (bd(A) has measure zero), there exists a closed rectangle B s.t A subset of B. So basically theyre saying, if bd(A) has measure zero then A is bounded. Can someone give me a quick proof of that? By the way when i say a set S has measure zero i mean for every e>0 there is a cover {U1,U2,...} of S by rectangles s.t. sum(i=1 to infinity)(volume(Ui)) < e.

2. Oct 29, 2006

Hurkyl

Staff Emeritus
Jordan measure only applies to bounded sets.

3. Oct 29, 2006

ak416

o ok my bad. But in general, if you have any set with its boundary being of measure zero, it doesnt necessarily mean its bounded right?

4. Oct 30, 2006

Hurkyl

Staff Emeritus
You are correct.

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