Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.restrict_le_restrict_iUnion
∀ {α : Type u_1} {m : MeasurableSpace α} {M : Type u_3} [inst : TopologicalSpace M] [inst_1 : AddCommMonoid M]
[inst_2 : PartialOrder M] [IsOrderedAddMonoid M] [OrderClosedTopology M] (v w : MeasureTheory.VectorMeasure α M)
{f : ℕ → Set α},
(∀ (n : ℕ), MeasurableSet (f n)) →
(∀ (n : ℕ), v.restrict (f n) ≤ w.restrict (f n)) → v.restrict (⋃ n, f n) ≤ w.restrict (⋃ n, f n)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
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
- 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
- Set.iUnionstatement and proof · cited by 2,483
- Disjointproof · cited by 2,201
- SummationFilter.unconditionalproof · cited by 2,068
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- tsumproof · cited by 1,148
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.exists_compl_positive_negativeproof · cited by 2
- MeasureTheory.VectorMeasure.restrict_le_restrict_countable_iUnionproof · cited by 1
- MeasureTheory.SignedMeasure.bddBelow_measureOfNegativesproof · cited by 1