Theorems · Theorem · measure theory
MeasureTheory.SignedMeasure.subset_negative_null_set
∀ {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 s u ≤ MeasureTheory.VectorMeasure.restrict 0 u →
s w = 0 → w ⊆ u → v ⊆ w → s v = 0A subset v of a null-set w has zero measure if w is a subset of a negative set u.
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- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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Cites12
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
- neg_zeroproof · cited by 542
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
- MeasureTheory.VectorMeasure.restrictstatement and proof · cited by 139
- MeasureTheory.SignedMeasurestatement and proof · cited by 108
- neg_applyproof · cited by 96
- MeasureTheory.VectorMeasure.neg_le_neg_iffproof · cited by 3
- MeasureTheory.SignedMeasure.subset_positive_null_setproof · cited by 2
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