nLab
pushforward measure

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Definition

In measure theory, the pushforward f *μf_\ast \mu of a measure μ\mu on a measurable space XX along a measurable function f:XYf \colon X \to Y to another measure space YY assigns to a subset the original measure of the preimage under ff of that subset:

(f *μ)()μ(f 1()). (f_\ast\mu)( - ) \coloneqq \mu(f^{-1}(-)) \,.

References

See also

Created on February 8, 2018 at 10:08:54. See the history of this page for a list of all contributions to it.