Timeline for What are your favorite instructional counterexamples?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 2, 2012 at 12:10 | comment | added | Connor Mooney | I should also mention here that $L^p$ convergence of $\{f_k\}$ to 0 implies that a subsequence converges pointwise a.e. to zero. To see this take a subsequence with $\int |f_k|^p < 2^{-k}$ (or any summable series) and use the monotone convergence theorem to conclude that $\int \sum |f_k|^p < \infty$. | |
| Jul 10, 2012 at 4:58 | comment | added | Douglas Zare | $\chi_{[0,1/2]}, \chi_{[1/2,5/6]}, \chi_{[5/6,1] \cup [0,1/12]}, \chi_{[1/12,17/60]}...$. | |
| May 19, 2012 at 13:53 | comment | added | Arch Stanton | I'm sorry, could I ask you to clarify what you mean by "characteristic functions of length $1/n$ wrapping around the interval $[0, 1]$". I ask as I thought $L^p$ convergence to zero did imply pwae convergence to $0$, so I would like to understand your example. | |
| Jul 30, 2011 at 16:38 | history | answered | Connor Mooney | CC BY-SA 3.0 |