Timeline for Linear independence of an odd set of measurable functions
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 1, 2016 at 16:59 | comment | added | ABIM | So what would that be then? | |
| Jul 22, 2016 at 15:30 | comment | added | Andreas Blass | Now that you've added "convex" to the question, a positive answer seems reasonably likely. | |
| Jul 22, 2016 at 9:36 | comment | added | Pietro Majer | If g is a constant, then those functions are linearly independent just because each is infinitesimal wrto the next. | |
| Jul 22, 2016 at 5:41 | comment | added | ABIM | That dounction isn't convex though, however I'm most interested in the case where $g(t)$ is constant anyway. | |
| Jul 22, 2016 at 5:40 | history | edited | ABIM | CC BY-SA 3.0 |
added 7 characters in body
|
| Jul 22, 2016 at 4:12 | comment | added | Andreas Blass | If you were considering functions defined just on the positive half of the real line, then your functions for $n=0$ and for $n=1$ could be linearly dependent; in fact, they could be equal if $g(t)=(t\cdot\ln t)/(t-1)$ (if I did the arithmetic right). This particular example doesn't work for negative $t$, but I wouldn't be surprised if more complicated dependences can occur on all of $\mathbb R$ for some maliciously designed functions $g(t)$. | |
| Jul 22, 2016 at 0:24 | history | edited | ABIM | CC BY-SA 3.0 |
added 60 characters in body
|
| Jul 22, 2016 at 0:16 | review | First posts | |||
| Jul 22, 2016 at 3:12 | |||||
| Jul 22, 2016 at 0:15 | history | asked | ABIM | CC BY-SA 3.0 |