Theorems · Theorem · measure theory

MeasureTheory.QuasiMeasurePreserving.prod_of_left

∀ {α : Type u_4} {β : Type u_5} {γ : Type u_6} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  [inst_2 : MeasurableSpace γ] {f : α × β → γ} {μ : MeasureTheory.Measure α} {ν : MeasureTheory.Measure β}
  {τ : MeasureTheory.Measure γ},
  Measurable f →
    ∀ [MeasureTheory.SFinite μ] [MeasureTheory.SFinite ν],
      (∀ᵐ (y : β) ∂ν, MeasureTheory.Measure.QuasiMeasurePreserving (fun x => f (x, y)) μ τ) →
        MeasureTheory.Measure.QuasiMeasurePreserving f (μ.prod ν) τ

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

3 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceMeasurableSpaceMeasurableSpaceMeasureTheory.SFiniteMeasureTheory.SFinite