Timeline for Compactness of sigma-algebra for the $L^1$ metrics
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 17, 2013 at 13:44 | comment | added | Martin | @Didier Piau: Dunford and Schwartz, Part I, Section III.7 has a paragraph The metric space $\Sigma(\mu)$ plus some exercises in III.9. It appears in the index "measure space, as a metric space". | |
| Mar 17, 2013 at 12:38 | comment | added | Did | @Rabee Thanks. What do you call "not compact in $L^1$"? Which part of Dunford and Schwartz? | |
| Mar 17, 2013 at 12:36 | comment | added | Did | @Julien Thanks for this answer. To which probability measures on [0,1], apart from the Lebesgue measure, does this apply? | |
| Mar 17, 2013 at 10:20 | comment | added | Rabee Tourky | The metric space $(G,d)$ is well treated in Dunford and Schwartz. Of course, it is not compact for atomless probability spaces because the interval $[0,1]$ is not compact in $L_1$. It is however complete which is sufficiently amazing. | |
| Mar 17, 2013 at 10:12 | history | answered | Julien Melleray | CC BY-SA 3.0 |