Theorems · Theorem · measure theory

MeasureTheory.NullMeasurableSet.preimage

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μa : MeasureTheory.Measure α}
  {μb : MeasureTheory.Measure β} {f : α → β} {s : Set β},
  MeasureTheory.NullMeasurableSet s μb →
    MeasureTheory.Measure.QuasiMeasurePreserving f μa μb → MeasureTheory.NullMeasurableSet (f ⁻¹' s) μa

The preimage of a null measurable set under a (quasi-)measure-preserving map is a null measurable set.

Defined in

Mathlib.MeasureTheory.Measure.QuasiMeasurePreserving

Cited by

21 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound