Theorems · Inductive type · measure theory

MeasureTheory.Measure.QuasiMeasurePreserving

{α : Type u_1} →
  {β : Type u_2} →
    {mβ : MeasurableSpace β} →
      {m0 : MeasurableSpace α} →
        (α → β) →
          autoParam (MeasureTheory.Measure α) MeasureTheory.Measure.QuasiMeasurePreserving._auto_1 →
            autoParam (MeasureTheory.Measure β) MeasureTheory.Measure.QuasiMeasurePreserving._auto_3 → Prop

A map f : α → β is said to be quasi-measure-preserving (a.k.a. non-singular) w.r.t. measures μa and μb if it is measurable and μb s = 0 implies μa (f ⁻¹' s) = 0.

Defined in

Mathlib.MeasureTheory.Measure.QuasiMeasurePreserving

Cited by

101 results in Mathlib

Foundations

Depth 9 from the axioms, rests on 34 definitions · uses no axioms