Theorems · Theorem · measure theory

MeasureTheory.Measure.QuasiMeasurePreserving.restrict

∀ {α : Type u_2} {β : Type u_3} {m0 : MeasurableSpace α} [inst : MeasurableSpace β] {μ : MeasureTheory.Measure α}
  {s : Set α} {ν : MeasureTheory.Measure β} {f : α → β},
  MeasureTheory.Measure.QuasiMeasurePreserving f μ ν →
    ∀ {t : Set β}, Set.MapsTo f s t → MeasureTheory.Measure.QuasiMeasurePreserving f (μ.restrict s) (ν.restrict t)

If a quasi-measure-preserving map f maps a set s to a set t, then it is quasi-measure-preserving with respect to the restrictions of the measures.

Defined in

Mathlib.MeasureTheory.Measure.Restrict

Cited by

1 results in Mathlib

Foundations

Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace