Theorems · Theorem · measure theory
BoxIntegral.Prepartition.measure_iUnion_toReal
∀ {ι : Type u_1} [Finite ι] {I : BoxIntegral.Box ι} (π : BoxIntegral.Prepartition I) (μ : MeasureTheory.Measure (ι → ℝ))
[MeasureTheory.IsLocallyFiniteMeasure μ], μ.real π.iUnion = ∑ J ∈ π.boxes, μ.real ↑J- Cited by
- 2 results in Mathlib
- Foundations
- Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealproof · cited by 9,879
- Finset.sumstatement and proof · cited by 5,195
- Finitestatement and proof · cited by 3,029
- Set.iUnionproof · cited by 2,483
- LT.lt.neproof · cited by 872
- ENNReal.toRealproof · cited by 859
- MeasureTheory.Measure.realstatement · cited by 530
- BoxIntegral.Boxstatement and proof · cited by 464
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.IntegrableOn.hasBoxIntegralproof · cited by 2
- BoxIntegral.HasIntegral.of_aeEq_zeroproof · cited by 1