Theorems · Definition · measure theory

MeasureTheory.Measure.comap

{α : Type u_1} →
  {β : Type u_2} →
    [inst : MeasurableSpace α] →
      [inst_1 : MeasurableSpace β] → (α → β) → MeasureTheory.Measure β → MeasureTheory.Measure α

Pullback of a Measure. If f sends each measurable set to a null-measurable set, then for each measurable set s we have comap f μ s = μ (f '' s). Note that if f is not injective, this definition assigns Set.univ measure zero.

Defined in

Mathlib.MeasureTheory.Measure.Comap

Cited by

96 results in Mathlib

Foundations

Depth 189 from the axioms, rests on 4,729 definitions · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpace