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function_integral [2015/06/20 16:16] nikolaj |
function_integral [2015/06/20 16:17] nikolaj |
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| | @#55CCEE: context | @#55CCEE: $\mathbb K = \overline{\mathbb R}\lor \mathbb C$ | | | @#55CCEE: context | @#55CCEE: $\mathbb K = \overline{\mathbb R}\lor \mathbb C$ | | ||
| | @#55CCEE: context | @#55CCEE: $\langle X,\Sigma,\mu\rangle\in \mathrm{MeasureSpace}(X)$ | | | @#55CCEE: context | @#55CCEE: $\langle X,\Sigma,\mu\rangle\in \mathrm{MeasureSpace}(X)$ | | ||
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| | @#FFBB00: definiendum | @#FFBB00: $\int_X: (X\to \mathbb K)\to \mathbb K$ | | | @#FFBB00: definiendum | @#FFBB00: $\int_X: (X\to \mathbb K)\to \mathbb K$ | | ||
| | @#FFBB00: definiendum | @#FFBB00: $\int_X\ f\ \mathrm d\mu:=\int_X\ (\mathrm{Re}f)^+\ \mathrm d\mu-\int_X\ (\mathrm{Re}f)^-\ \mathrm d\mu+i\ \left( \int_X\ (\mathrm{Im}f)^+\ \mathrm d\mu-\ \int_X\ (\mathrm{Im}f)^-\ \mathrm d\mu \right)$ | | | @#FFBB00: definiendum | @#FFBB00: $\int_X\ f\ \mathrm d\mu:=\int_X\ (\mathrm{Re}f)^+\ \mathrm d\mu-\int_X\ (\mathrm{Re}f)^-\ \mathrm d\mu+i\ \left( \int_X\ (\mathrm{Im}f)^+\ \mathrm d\mu-\ \int_X\ (\mathrm{Im}f)^-\ \mathrm d\mu \right)$ | | ||
