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integral_over_a_subset [2014/02/13 16:13] 127.0.0.1 external edit |
integral_over_a_subset [2014/02/25 20:51] nikolaj |
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| @#88DDEE: $\mathbb K = \overline{\mathbb R}\lor \mathbb C$ | | | @#88DDEE: $\mathbb K = \overline{\mathbb R}\lor \mathbb C$ | | ||
| @#88DDEE: $\langle X,\Sigma,\mu_X\rangle$ ... measure space | | | @#88DDEE: $\langle X,\Sigma,\mu_X\rangle$ ... measure space | | ||
- | | @#88DDEE: $S\subset X$ | | ||
- | | @#FFBB00: $\int_S: (X\to \mathbb K)\to \mathbb K$ | | + | | @#FFBB00: $\int_S: \mathcal P(X)\to(X\to \mathbb K)\to \mathbb K$ | |
- | | $f: X\to \mathbb K$ | | + | | @#DDDDDD: $f: X\to \mathbb K$ | |
| @#FFBB00: $\int_S\ f\ \mathrm d\mu_X:=\int_X\ f\cdot \chi_S\ \mathrm d\mu_X$ | | | @#FFBB00: $\int_S\ f\ \mathrm d\mu_X:=\int_X\ f\cdot \chi_S\ \mathrm d\mu_X$ | |