Timeline for Measure Theories with a different convention to $\infty\cdot 0 =0$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 23, 2020 at 21:46 | comment | added | Alan | @NikWeaver so we cannot have a measure theory with $\infty \cdot 0 = \infty$? I don't see how do you preclude it? | |
| May 13, 2020 at 3:02 | comment | added | Nik Weaver | @NateEldredge right, exactly. | |
| May 13, 2020 at 2:51 | comment | added | Nate Eldredge | Another way to say it is that the integral of the given $f$ is zero no matter how you define $0 \cdot \infty$. Adopting that convention just means that you can write a more compact expression for the integral of $f = c \cdot 1_A$, one which doesn't require $c=\infty$ or $m(A)=\infty$ to be special cases. But measure theory doesn't change in any way if you use a different convention. | |
| May 13, 2020 at 2:38 | history | answered | Nik Weaver | CC BY-SA 4.0 |