===== Function integral =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $\mathbb K = \overline{\mathbb R}\lor \mathbb C$ |
| @#55CCEE: context     | @#55CCEE: $\langle X,\Sigma,\mu\rangle\in \mathrm{MeasureSpace}(X)$ |
| @#FFBB00: definiendum | @#FFBB00: $\int_X: (X\to \mathbb K)\to \mathbb K$ |
| @#FFBB00: definiendum | @#FFBB00: $\int_X\ f\ \mathrm d\mu:=\int_X\ (\mathrm{Re}f)^+\ \mathrm d\mu-\int_X\ (\mathrm{Re}f)^-\ \mathrm d\mu+i\ \left( \int_X\ (\mathrm{Im}f)^+\ \mathrm d\mu-\ \int_X\ (\mathrm{Im}f)^-\ \mathrm d\mu \right)$ |

Notice that the integral on the right hand side here is that for positive measurable numerical functions. 

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=== Context ===
[[Positive function integral]], 
[[Positive part of a function]], 
[[Negative part of a function]], 
[[Real part of a function]], 
[[Imaginary part of a function]],