Theorems · Theorem · measure theory
MeasureTheory.JordanDecomposition.real_smul_posPart_nonneg
∀ {α : Type u_1} [inst : MeasurableSpace α] (j : MeasureTheory.JordanDecomposition α) (r : ℝ),
0 ≤ r → (r • j).posPart = r.toNNReal • j.posPart- Cited by
- 0 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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Cites10
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
- Real.toNNRealstatement and proof · cited by 267
- 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
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