Theorems · Theorem · measure theory

MeasureTheory.Measure.infinitePi_map_curry_symm

∀ {ι : Type u_6} {κ : Type u_7} {X : Type u_8} {mX : MeasurableSpace X} (μ : ι → κ → MeasureTheory.Measure X)
  [hμ : ∀ (i : ι) (j : κ), MeasureTheory.IsProbabilityMeasure (μ i j)],
  MeasureTheory.Measure.map (⇑(MeasurableEquiv.curry ι κ X).symm)
      (MeasureTheory.Measure.infinitePi fun i => MeasureTheory.Measure.infinitePi fun j => μ i j) =
    MeasureTheory.Measure.infinitePi fun p => μ p.1 p.2

Defined in

Mathlib.Probability.ProductMeasure

Cited by

1 results in Mathlib

Foundations

Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.IsProbabilityMeasure