Theorems · Theorem · measure theory
MeasureTheory.JordanDecomposition.real_smul_negPart_neg
∀ {α : Type u_1} [inst : MeasurableSpace α] (j : MeasureTheory.JordanDecomposition α),
∀ r < 0, (r • j).negPart = (-r).toNNReal • j.posPart- Cited by
- 2 results in Mathlib
- Foundations
- Depth 182 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- NNRealstatement · cited by 4,310
- not_leproof · cited by 328
- Real.toNNRealstatement and proof · cited by 267
- MeasureTheory.JordanDecomposition.negPartstatement and proof · cited by 44
- MeasureTheory.JordanDecomposition.posPartstatement and proof · cited by 43
- MeasureTheory.JordanDecompositionstatement and proof · cited by 40
- MeasureTheory.JordanDecomposition.real_smul_defproof · cited by 5
- MeasureTheory.JordanDecomposition.smul_posPartproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.singularPart_smulproof · cited by 1
- MeasureTheory.SignedMeasure.toJordanDecomposition_smul_realproof · cited by 1