Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.restrict_le_zero_subset
∀ {α : Type u_1} {m : MeasurableSpace α} {M : Type u_3} [inst : TopologicalSpace M] [inst_1 : AddCommMonoid M]
[inst_2 : PartialOrder M] (v : MeasureTheory.VectorMeasure α M) {i j : Set α},
MeasurableSet i →
j ⊆ i →
v.restrict i ≤ MeasureTheory.VectorMeasure.restrict 0 i → v.restrict j ≤ MeasureTheory.VectorMeasure.restrict 0 j- Cited by
- 2 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
- Set.Subset.transproof · cited by 218
- MeasureTheory.VectorMeasure.restrictstatement and proof · cited by 139
- MeasureTheory.VectorMeasure.restrict_le_restrict_iffproof · cited by 12
- MeasureTheory.VectorMeasure.restrict_le_restrict_of_subset_leproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.exists_compl_positive_negativeproof · cited by 2
- MeasureTheory.SignedMeasure.bddBelow_measureOfNegativesproof · cited by 1