Theorems · Theorem · measure theory
MeasureTheory.Measure.le_iff
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ₁ μ₂ : MeasureTheory.Measure α},
μ₁ ≤ μ₂ ↔ ∀ (s : Set α), MeasurableSet s → μ₁ s ≤ μ₂ s- Cited by
- 21 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasurableSetstatement · cited by 3,075
- MeasureTheory.Measure.outerMeasure_le_iffproof · cited by 3
Cited by21
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.restrict_le_selfproof · cited by 57
- MeasureTheory.VectorMeasure.variation_restrictproof · cited by 14
- MeasureTheory.Measure.le_sumproof · cited by 9
- MeasureTheory.Measure.restrict_sub_eq_restrict_sub_restrictproof · cited by 6
- MeasureTheory.Measure.le_introproof · cited by 6
- MeasureTheory.Measure.restrict_iUnion_leproof · cited by 5
- MeasureTheory.Measure.restrict_mono'proof · cited by 3
- MeasureTheory.withDensity_monoproof · cited by 3
- MeasureTheory.exists_isHahnDecompositionproof · cited by 3
- MeasurableEmbedding.variation_mapproof · cited by 3
- MeasureTheory.Measure.map_monoproof · cited by 3
- MeasureTheory.Measure.restrict_union_leproof · cited by 3