volume_measurePreserving_sumPiEquivProdPi

English

The volume is preserved by the symmetric sumPiEquivProdPi construction.

Русский

Объем сохраняется при симметричной SumPiEquivProdPi конструкции.

LaTeX

$$volume_preserving_sumPiEquivProdPi_symm (X) :$$

Lean4

theorem volume_measurePreserving_sumPiEquivProdPi (X : ι ⊕ ι' → Type*) [∀ i, MeasureSpace (X i)]
    [∀ i, SigmaFinite (volume : Measure (X i))] :
    MeasurePreserving (MeasurableEquiv.sumPiEquivProdPi X) volume volume :=
  measurePreserving_sumPiEquivProdPi (fun _ ↦ volume)

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