Category:Pushforward Measures
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This category contains results about Pushforward Measures.
Definitions specific to this category can be found in Definitions/Pushforward Measures.
Let $\struct {X, \Sigma}$ and $\struct {X', \Sigma'}$ be measurable spaces.
Let $\mu$ be a measure on $\struct {X, \Sigma}$.
Let $f: X \to X'$ be a $\Sigma \, / \, \Sigma'$-measurable mapping.
Then the pushforward of $\mu$ under $f$ is the mapping $f_* \mu: \Sigma' \to \overline \R$ defined by:
- $\forall E' \in \Sigma': \map {f_* \mu} {E'} := \map \mu {f^{-1} \sqbrk {E'} }$
where $\overline \R$ denotes the extended real numbers.
Subcategories
This category has only the following subcategory.
Pages in category "Pushforward Measures"
The following 2 pages are in this category, out of 2 total.