Proof of Boundedness for Sets with Measure Zero?

[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.

 

[Hurkyl]

Jordan measure only applies to bounded sets.

 

[ak416]

o ok my bad. But in general, if you have any set with its boundary being of measure zero, it doesn't necessarily mean its bounded right?

 

[Hurkyl]

You are correct.