Category:Integral with respect to Pushforward Measure
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This category contains pages concerning Integral with respect to Pushforward Measure:
Let $\struct {X, \Sigma, \mu}$ be a measure space.
Let $\struct {X', \Sigma'}$ be a measurable space.
Let $T: X \to X'$ be a $\Sigma \, / \, \Sigma'$-measurable mapping.
Let $f: X' \to \overline \R$ be a positive $\Sigma'$-measurable function.
Let $\map T \mu$ be the pushforward measure of $\mu$ under $T$.
Then $f \circ T: X \to \overline \R$ is positive and $\Sigma$-measurable with:
- $\ds \int_{X'} f \rd \map T \mu = \int_X f \circ T \rd \mu$
Pages in category "Integral with respect to Pushforward Measure"
The following 2 pages are in this category, out of 2 total.