Theorems · Theorem · measure theory
MeasureTheory.JordanDecomposition.smul_negPart
∀ {α : Type u_1} [inst : MeasurableSpace α] (j : MeasureTheory.JordanDecomposition α) (r : NNReal),
(r • j).negPart = r • j.negPart- Cited by
- 5 results in Mathlib
- Foundations
- Depth 180 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.
Cites6
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 · cited by 10,939
- ENNRealstatement · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- MeasureTheory.JordanDecomposition.negPartstatement · cited by 44
- MeasureTheory.JordanDecompositionstatement and proof · cited by 40
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.JordanDecomposition.real_smul_posPart_negproof · cited by 2
- MeasureTheory.SignedMeasure.singularPart_smul_nnrealproof · cited by 1
- MeasureTheory.SignedMeasure.toJordanDecomposition_smul_realproof · cited by 1
- MeasureTheory.JordanDecomposition.toSignedMeasure_smulproof · cited by 1
- MeasureTheory.JordanDecomposition.real_smul_negPart_nonnegproof · cited by 0