Theorems · Theorem · measure theory
MeasureTheory.SignedMeasure.singularPart_mutuallySingular
∀ {α : Type u_1} {m : MeasurableSpace α} (s : MeasureTheory.SignedMeasure α) (μ : MeasureTheory.Measure α),
(s.toJordanDecomposition.posPart.singularPart μ).MutuallySingular (s.toJordanDecomposition.negPart.singularPart μ)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- le_rflproof · cited by 1,558
- MeasureTheory.SignedMeasurestatement and proof · cited by 108
- MeasureTheory.Measure.MutuallySingularstatement · cited by 91
- MeasureTheory.Measure.singularPartstatement · cited by 71
- MeasureTheory.JordanDecomposition.negPartstatement and proof · cited by 44
- MeasureTheory.JordanDecomposition.posPartstatement · cited by 43
- MeasureTheory.SignedMeasure.toJordanDecompositionstatement and proof · cited by 34
- MeasureTheory.Measure.singularPart_leproof · cited by 7
- MeasureTheory.Measure.MutuallySingular.monoproof · cited by 3
- MeasureTheory.JordanDecomposition.mutuallySingularproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.singularPart_totalVariationproof · cited by 1