Theorems · Theorem · measure theory
MeasureTheory.SignedMeasure.toJordanDecomposition_neg
∀ {α : Type u_1} [inst : MeasurableSpace α] (s : MeasureTheory.SignedMeasure α),
(-s).toJordanDecomposition = -s.toJordanDecomposition- Cited by
- 3 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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.
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.SignedMeasurestatement and proof · cited by 108
- MeasureTheory.JordanDecompositionstatement · cited by 40
- MeasureTheory.SignedMeasure.toJordanDecompositionstatement and proof · cited by 34
- MeasureTheory.SignedMeasure.toSignedMeasure_toJordanDecompositionproof · cited by 10
- MeasureTheory.JordanDecomposition.toSignedMeasure_injectiveproof · cited by 6
- MeasureTheory.JordanDecomposition.toSignedMeasure_negproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.singularPart_negproof · cited by 2
- MeasureTheory.SignedMeasure.toJordanDecomposition_smul_realproof · cited by 1
- MeasureTheory.SignedMeasure.totalVariation_negproof · cited by 0