Theorems · Theorem · measure theory

MeasureTheory.QuasiMeasurePreserving.prodMap

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  [inst_2 : MeasurableSpace γ] {μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β} {τ : MeasureTheory.Measure γ}
  {ω : Type u_4} {mω : MeasurableSpace ω} {υ : MeasureTheory.Measure ω} [MeasureTheory.SFinite μ]
  [MeasureTheory.SFinite τ] [MeasureTheory.SFinite υ] {f : α → β} {g : γ → ω},
  MeasureTheory.Measure.QuasiMeasurePreserving f μ ν →
    MeasureTheory.Measure.QuasiMeasurePreserving g τ υ →
      MeasureTheory.Measure.QuasiMeasurePreserving (Prod.map f g) (μ.prod τ) (ν.prod υ)

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

0 results in Mathlib

Foundations

Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasurableSpaceMeasureTheory.SFiniteMeasureTheory.SFiniteMeasureTheory.SFinite