Theorems · Inductive type · measure theory
MeasureTheory.IsHahnDecomposition
{α : Type u_1} → {mα : MeasurableSpace α} → MeasureTheory.Measure α → MeasureTheory.Measure α → Set α → PropA set where μ ≤ ν (and the reverse inequality on the complement),
defined via measurable set and measure restriction comparisons.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- MeasurableSpacestatement · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
Cited by12
Results whose statement or proof uses this declaration.
- MeasureTheory.IsHahnDecomposition.measurableSetstatement and proof · cited by 6
- MeasureTheory.IsHahnDecomposition.le_onstatement and proof · cited by 4
- MeasureTheory.exists_isHahnDecompositionstatement · cited by 3
- MeasureTheory.IsHahnDecomposition.complstatement and proof · cited by 2
- MeasureTheory.IsHahnDecomposition.ge_on_complstatement and proof · cited by 2
- MeasureTheory.Measure.sub_apply_eq_zero_of_isHahnDecompositionstatement and proof · cited by 2
- MeasureTheory.Measure.toSignedMeasure_restrict_substatement and proof · cited by 1
- MeasureTheory.Measure.sub_toSignedMeasure_eq_toSignedMeasure_subproof · cited by 0
- MeasureTheory.IsHahnDecomposition.casesOnstatement and proof · cited by 0
- MeasureTheory.IsHahnDecomposition.recOnstatement and proof · cited by 0
- MeasureTheory.Measure.sub_le_iff_le_addproof · cited by 0
- MeasureTheory.Measure.mutually_singular_measure_subproof · cited by 0