Theorems · Theorem · measure theory
MeasureTheory.VectorMeasure.le_iff
∀ {α : Type u_1} {m : MeasurableSpace α} {M : Type u_3} [inst : TopologicalSpace M] [inst_1 : AddCommMonoid M]
[inst_2 : PartialOrder M] {v w : MeasureTheory.VectorMeasure α M}, v ≤ w ↔ ∀ (i : Set α), MeasurableSet i → v i ≤ w i- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · 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 · cited by 3,075
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.restrict_le_restrict_iffproof · cited by 12
- MeasureTheory.Measure.toSignedMeasure_le_toSignedMeasure_iffproof · cited by 0