Theorems · Theorem · measure theory
MeasureTheory.SignedMeasure.of_inter_eq_of_symmDiff_eq_zero_positive
∀ {α : Type u_1} [inst : MeasurableSpace α] {s : MeasureTheory.SignedMeasure α} {u v w : Set α},
MeasurableSet u →
MeasurableSet v →
MeasurableSet w →
MeasureTheory.VectorMeasure.restrict 0 u ≤ MeasureTheory.VectorMeasure.restrict s u →
MeasureTheory.VectorMeasure.restrict 0 v ≤ MeasureTheory.VectorMeasure.restrict s v →
s (symmDiff u v) = 0 → s (w ∩ u) = s (w ∩ v)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasurableSetstatement and proof · cited by 3,075
- zero_addproof · cited by 2,366
- MeasureTheory.VectorMeasurestatement · cited by 451
- Set.inter_subset_rightproof · cited by 329
- symmDiffstatement and proof · cited by 236
- MeasurableSet.interproof · cited by 167
- MeasureTheory.VectorMeasure.restrictstatement and proof · cited by 139
- MeasureTheory.SignedMeasurestatement and proof · cited by 108
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.JordanDecomposition.toSignedMeasure_injectiveproof · cited by 6
- MeasureTheory.SignedMeasure.of_inter_eq_of_symmDiff_eq_zero_negativeproof · cited by 0