#
nLab

pushforward measure

Contents
### Context

#### Measure and probability theory

# Contents

## Definition

In measure theory, the *pushforward* $f_\ast \mu$ of a measure $\mu$ on a measurable space $X$ along a measurable function $f \colon X \to Y$ to another measure space $Y$ assigns to a subset the original measure of the preimage under $f$ of that subset:

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

## References

See also

Created on February 8, 2018 at 10:08:54.
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