0
$\begingroup$

I'm trying to give an example of a bounded set of measure zero that is rectifiable and an example of a bounded set of measure zero that is not rectifiable.

I can't think of 1 the top of my head, and for a susbet S of R^n to be rectifiable, we need to have S bounded and BdS measure zero.

  • 1
    Uh, why did you flag your own question? Is that a misclick?2012-02-28

1 Answers 1

1

Rectifiables are somewhat easier to find, so we'll leave them aside for now. As for a non-rectifiable set of measure $0$, you might want to take a look at the set $\mathbb{Q}\cap(0,1)$. This is a concrete and canonical example to the comment of Dave Renfro above.