Theorems · Theorem · measure theory
MeasureTheory.measureReal_union_le
∀ {α : Type u_1} {x : MeasurableSpace α} {μ : MeasureTheory.Measure α} (s₁ s₂ : Set α),
μ.real (s₁ ∪ s₂) ≤ μ.real s₁ + μ.real s₂- Defined in
- Mathlib.MeasureTheory.Measure.Real
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- Top.topproof · cited by 9,680
- LT.lt.neproof · cited by 872
- ENNReal.toRealproof · cited by 859
- MeasureTheory.Measure.realstatement · cited by 530
- Set.subset_union_leftproof · cited by 142
- Set.subset_union_rightproof · cited by 123
- add_nonnegproof · cited by 104
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.measureReal_union_nullproof · cited by 1
- MeasureTheory.le_measureReal_sdiffproof · cited by 1
- MeasureTheory.measureReal_biUnion_finset_leproof · cited by 1
- MeasureTheory.measureReal_symmDiff_leproof · cited by 0