Theorems · Theorem · measure theory
MeasureTheory.measureReal_union_null
∀ {α : Type u_1} {x : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s₁ s₂ : Set α},
μ.real s₁ = 0 → μ.real s₂ = 0 → μ.real (s₁ ∪ s₂) = 0- Defined in
- Mathlib.MeasureTheory.Measure.Real
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- LE.le.transproof · cited by 3,151
- add_zeroproof · cited by 2,707
- le_antisymmproof · cited by 2,068
- MeasureTheory.Measure.realstatement and proof · cited by 530
- MeasureTheory.measureReal_nonnegproof · cited by 21
- MeasureTheory.measureReal_union_leproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.measureReal_union_null_iffproof · cited by 0