Timeline for Counterexample of non-negative sequence weakly converging in $\mathscr{M}^1$ but not $L^1$
Current License: CC BY-SA 3.0
8 events
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| May 27, 2013 at 6:28 | vote | accept | Ayman Moussa | ||
| May 24, 2013 at 17:53 | history | edited | Gerald Edgar | CC BY-SA 3.0 |
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| May 24, 2013 at 16:34 | comment | added | Ayman Moussa | I may won't have access often to internet in the coming days, but I thank you all for you answers and good ideas, and will carefully read them asap. | |
| May 24, 2013 at 16:32 | comment | added | Ayman Moussa | Thank you Gerald for this detailed and very well written answer. I still have one question though. Could you detail a bit the equality of the integrals on $I$, for $k>n$ ? $\alpha$ is defined as a limit and appears in the definition of $f$, so I can't understand how this equality may be true for $n$ "large enough" (meaning, wuthiut any passage to the limit). Also, your counterxample, such as the one of Bill, suggests that my proof above is wrong (it is supposed to work in the case where the limit function is bounded), any hint for the mistake is also welcome ! | |
| May 24, 2013 at 14:19 | history | edited | Gerald Edgar | CC BY-SA 3.0 |
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| May 24, 2013 at 14:12 | history | edited | Gerald Edgar | CC BY-SA 3.0 |
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| May 24, 2013 at 13:49 | history | edited | Gerald Edgar | CC BY-SA 3.0 |
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| May 24, 2013 at 13:40 | history | answered | Gerald Edgar | CC BY-SA 3.0 |