Timeline for Measure induced by function
Current License: CC BY-SA 3.0
10 events
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| Jun 30, 2013 at 20:21 | comment | added | randomsample | the function $-xy-yz-xz$ was just one example. I was only wondering if one can say in general that the 2-marginals are negative if $f$ has the properties above. Maybe $f(x,y,z) = -\frac{1}{xyz}$ on $[1,\infty)^3$ is a better example. | |
| Jun 30, 2013 at 19:56 | comment | added | randomsample | The 2-dimensional marginal of the 3-dimensional Lebesgue measure is a 2-dimensional Lebesgue measure. So I do not see why the 2-dimensional marginals of $\mu$ should be 0? | |
| Jun 30, 2013 at 19:27 | comment | added | Gerald Edgar | The example cited, $f(x,y,z) = -xy-yz-xz$, assigns measure zero to all $3$-rectangles. | |
| Jun 30, 2013 at 15:28 | comment | added | Asaf | The 2-dimensional sections you've mentioned are of 0 Lebesgue measure (hence of $0$ $f$ measure, becuase it is ac measure wrt to Lebesgue), so they will be "ignored" by the Hahn decomposition of the $f$ measure, which will be essentially $P=[0,\infty)^{3}$. I think this is not a research-level question, as stated currently. | |
| Jun 30, 2013 at 15:22 | history | edited | Dan Piponi | CC BY-SA 3.0 |
edited title
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| Jun 30, 2013 at 12:11 | comment | added | randomsample | if the function $f$ is differentiable that is equivalent to $\frac{\partial f}{\partial x_i x_j x_m} \geq 0$ | |
| Jun 30, 2013 at 12:10 | comment | added | randomsample | en.wikipedia.org/wiki/N-increasing | |
| Jun 30, 2013 at 12:03 | comment | added | Michael Greinecker | What does "3-increasing" mean? | |
| Jun 30, 2013 at 11:34 | review | First posts | |||
| Jun 30, 2013 at 11:35 | |||||
| Jun 30, 2013 at 11:18 | history | asked | randomsample | CC BY-SA 3.0 |