Timeline for Is arbitrary union of closed balls in $\mathbb{R}^n$ Lebesgue measurable?
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| Oct 26, 2010 at 23:09 | comment | added | Amit Kumar Gupta | You can't approximate an arbitrary closed ball with a union from a countable collection of closed balls. For instance, suppose you were tempted to take as your collection $\mathcal{C}$ the closed balls of rational radius centered at a point with rational coordinates. Let $B$ be an arbitrary closed ball. You would need $B = \bigcup _{B' \in \mathcal{C}, B' \subset B} B'$. It's easy to see that for $x$ in the boundary of $B$, $x$ lies in that union iff $x$ has rational coordinates, but of course most of the points on the boundary won't. | |
| Oct 26, 2010 at 22:36 | history | edited | Gerhard Paseman | CC BY-SA 2.5 |
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| Oct 26, 2010 at 22:33 | comment | added | George Lowther | You can't replace by a countable union - for example see my comment to the question. | |
| Oct 26, 2010 at 22:31 | history | answered | Gerhard Paseman | CC BY-SA 2.5 |