##  [Pushforward (Image) Measure](/pushforward-image-measure) 

  ##  [Pushforward (Image) Measure](https://natural.quantumdictionary.io/pushforward-image-measure-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Given a measurable map f : (X, Σ_X) → (Y, Σ_Y) and a measure μ on X, the pushforward (image) measure f_*μ on Y is defined by f_*μ(B)=μ(f^{-1}(B)) for measurable B⊂Y; it is the natural way to transport mass under f.