Theorems · Theorem · measure theory

MeasureTheory.measurePreserving_prodAssoc

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  [inst_2 : MeasurableSpace γ] (μa : MeasureTheory.Measure α) (μb : MeasureTheory.Measure β)
  (μc : MeasureTheory.Measure γ) [MeasureTheory.SFinite μb] [MeasureTheory.SFinite μc],
  MeasureTheory.MeasurePreserving (⇑MeasurableEquiv.prodAssoc) ((μa.prod μb).prod μc) (μa.prod (μb.prod μc))

The measurable equiv induced by the equiv (α × β) × γ ≃ α × (β × γ) is measure preserving.

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

1 results in Mathlib

Foundations

Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceMeasurableSpaceMeasurableSpaceMeasureTheory.SFiniteMeasureTheory.SFinite