Theorems · Theorem · measure theory
MeasureTheory.JordanDecomposition.real_smul_def
∀ {α : Type u_1} [inst : MeasurableSpace α] (r : ℝ) (j : MeasureTheory.JordanDecomposition α),
r • j = if 0 ≤ r then r.toNNReal • j else -((-r).toNNReal • j)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 181 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.
Cites5
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
- NNRealstatement · cited by 4,310
- Real.toNNRealstatement · cited by 267
- MeasureTheory.JordanDecompositionstatement and proof · cited by 40
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.JordanDecomposition.real_smul_negPart_negproof · cited by 2
- MeasureTheory.JordanDecomposition.real_smul_posPart_negproof · cited by 2
- MeasureTheory.JordanDecomposition.coe_smulproof · cited by 0
- MeasureTheory.JordanDecomposition.real_smul_negPart_nonnegproof · cited by 0
- MeasureTheory.JordanDecomposition.real_smul_posPart_nonnegproof · cited by 0