Timeline for Defining the integral of a function using the product measure
Current License: CC BY-SA 3.0
6 events
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| Mar 24, 2014 at 17:21 | comment | added | Pietro Majer | You don't even need the construction of the product measure, even for integrals on a general measure space $(X,\mu)$: you may define the integral of a measurable $f:X\to[0,\infty]$ as the (Riemann) integral of its distribution function (a decreasing function): $$\int_X f(x) d\mu(x)=\int_0^\infty\mu\{f>t\}dt .$$ But the same remark in Jochen's answer holds, even for the simple case of the Lebesgue measure on $[0,1]$: doing something out of this definition turns out to be quite hard. | |
| Mar 24, 2014 at 16:41 | answer | added | berlin | timeline score: 1 | |
| Sep 6, 2012 at 7:54 | vote | accept | goblin GONE | ||
| Aug 30, 2012 at 17:06 | answer | added | Nik Weaver | timeline score: 2 | |
| Aug 30, 2012 at 12:44 | answer | added | Jochen Wengenroth | timeline score: 5 | |
| Aug 30, 2012 at 12:22 | history | asked | goblin GONE | CC BY-SA 3.0 |