Measurable function

Pushforward measure

Let (𝑋,Σ,𝜇) be a measure space, (𝑌,T) be a measurable space, and 𝑓 :𝑋 →𝑌 is a measurable function, then the pushforward measure on 𝑌 is given by measure

𝑓∗𝜇=𝜇∘(𝑓−1↾T)

i.e. 𝑓∗𝜇(𝐴) =𝜇𝑓−1(𝐴).

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