Theorems · Theorem · measure theory

MeasureTheory.Measure.pi_univ

∀ {ι : Type u_1} {α : ι → Type u_3} [inst : Fintype ι] [inst_1 : (i : ι) → MeasurableSpace (α i)]
  (μ : (i : ι) → MeasureTheory.Measure (α i)) [∀ (i : ι), MeasureTheory.SigmaFinite (μ i)],
  (MeasureTheory.Measure.pi μ) Set.univ = ∏ i, (μ i) Set.univ

Defined in: Mathlib.MeasureTheory.Constructions.Pi
Cited by: 1 results in Mathlib
Foundations: Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype MeasurableSpace MeasureTheory.SigmaFinite

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Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement and proof · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement and proof · cited by 9,879
Fintypestatement and proof · cited by 7,736
Set.univstatement and proof · cited by 3,945
Finset.univstatement and proof · cited by 3,473
Finset.prodstatement and proof · cited by 2,356
MeasureTheory.SigmaFinitestatement and proof · cited by 526
MeasureTheory.Measure.pistatement and proof · cited by 130
MeasureTheory.Measure.pi_piproof · cited by 31

Cited by1

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.setLIntegral_paramSet_expproof · cited by 1