Timeline for Does a submanifold of nonzero codimension have measure zero under the product of non atomic measures?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 26, 2021 at 10:24 | vote | accept | Nate River | ||
| Dec 26, 2021 at 10:22 | comment | added | Nate River | Oh, its literally only a permutation of coordinates, instead of a more general transformation. That makes sense, thanks! I actually did not know you could always write it this way as a graph with only a permutation of coordinates. @Yuval Peres | |
| Dec 26, 2021 at 10:07 | comment | added | Yuval Peres | Permuting the coordinates preserves the product measure $A \times\ldots \times A$. And this is just a notational device so the map $f$ takes the first $n-1$ coordinates to the last one. | |
| Dec 26, 2021 at 5:54 | comment | added | user130903 | @Nate River: You just permute the coordinates, relative to which it is a product of measures. So you really only permute these non-atomic measures. | |
| Dec 26, 2021 at 0:33 | comment | added | Nate River | Hm, the comment on the graph having measure $0$ by Fubini - this implicitly assumes that the induced measure after permuting the coordinates is still a product of nonatomic measures right? How does one see this? | |
| Dec 25, 2021 at 17:29 | history | edited | Yuval Peres | CC BY-SA 4.0 |
added 115 characters in body
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| Dec 25, 2021 at 17:08 | history | answered | Yuval Peres | CC BY-SA 4.0 |