Timeline for Existence of a certain norm on space of measurable functions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 19, 2017 at 11:57 | vote | accept | Learner | ||
| Nov 19, 2017 at 5:18 | answer | added | R W | timeline score: 1 | |
| Nov 18, 2017 at 22:46 | comment | added | Nate Eldredge | I think at a minimum you need $\phi$ to be concave. For instance consider $\phi(t) = t^2$. If we take $X =\mathbb{R}$ with Lebesgue measure, we would have to have $\|\chi_{[0,1)} + \chi_{[1,2]}\| = \|\chi_{[0,2]}\| = 4 > 2 = \|\chi_{[0,1)}\| + \|\chi_{[1,2]}\|$ contradicting the triangle inequality for the norm. | |
| Nov 18, 2017 at 20:02 | review | First posts | |||
| Nov 18, 2017 at 20:05 | |||||
| Nov 18, 2017 at 19:59 | history | asked | Learner | CC BY-SA 3.0 |