Theorems · Theorem · measure theory

MeasureTheory.Measure.map_prod_map

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β]
  [inst_2 : MeasurableSpace γ] {δ : Type u_4} [inst_3 : MeasurableSpace δ] {f : α → β} {g : γ → δ}
  (μa : MeasureTheory.Measure α) (μc : MeasureTheory.Measure γ) [MeasureTheory.SFinite μa] [MeasureTheory.SFinite μc],
  Measurable f →
    Measurable g →
      (MeasureTheory.Measure.map f μa).prod (MeasureTheory.Measure.map g μc) =
        MeasureTheory.Measure.map (Prod.map f g) (μa.prod μc)

Defined in

Mathlib.MeasureTheory.Measure.Prod

Cited by

7 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceMeasurableSpaceMeasurableSpaceMeasurableSpaceMeasureTheory.SFiniteMeasureTheory.SFinite