Function integral
Set
| context | $\mathbb K = \overline{\mathbb R}\lor \mathbb C$ |
| context | $\langle X,\Sigma,\mu\rangle\in \mathrm{MeasureSpace}(X)$ |
| definiendum | $\int_X: (X\to \mathbb K)\to \mathbb K$ |
| definiendum | $\int_X\ f\ \mathrm d\mu:=\int_X\ (\mathrm{Re}f)^+\ \mathrm d\mu-\int_X\ (\mathrm{Re}f)^-\ \mathrm d\mu+i\ \left( \int_X\ (\mathrm{Im}f)^+\ \mathrm d\mu-\ \int_X\ (\mathrm{Im}f)^-\ \mathrm d\mu \right)$ |
Notice that the integral on the right hand side here is that for positive measurable numerical functions.
Context
Positive function integral, Positive part of a function, Negative part of a function, Real part of a function, Imaginary part of a function,
