Timeline for Is it consistent with ZFC that some translation-invariant extension of Lebesgue measure assigns nonzero measure to some set of cardinality $<\frak c$?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 26, 2013 at 19:10 | comment | added | Alexander Pruss | The proof more generally shows that there is no quasi-translation-invariant (preserves null-measure under translations) $\sigma$-finite measure on $\mathbb R$ that assigns a nonzero measure to a set of cardinality less than $c$. Nice to know this fact. | |
| Mar 25, 2013 at 23:42 | vote | accept | Alexander Pruss | ||
| Mar 25, 2013 at 22:17 | comment | added | Joseph Van Name | You can also just take the additive subgroup of $B$. I just used vector spaces out of personal preference since $\mathbb{R}$ is a vector space over $\mathbb{Q}$. | |
| Mar 25, 2013 at 22:01 | comment | added | Alexander Pruss | Should the "vector subspace of $\mathbb R$ generated by $A$" just be the additive subgroup generated by $B$? Then (after fixing some typos) this looks like it should work. I think it's also simpler than the proofs that I've seen of the fact that every Lebesgue measurable subset of positive measure has cardinality $c$. Is there a reference for this proof? | |
| Mar 25, 2013 at 21:51 | history | edited | Joseph Van Name | CC BY-SA 3.0 |
added 157 characters in body
|
| Mar 25, 2013 at 21:41 | history | answered | Joseph Van Name | CC BY-SA 3.0 |