Theorems · Theorem · measure theory
MeasureTheory.SignedMeasure.not_haveLebesgueDecomposition_iff
∀ {α : Type u_1} {m : MeasurableSpace α} (s : MeasureTheory.SignedMeasure α) (μ : MeasureTheory.Measure α),
¬s.HaveLebesgueDecomposition μ ↔
¬s.toJordanDecomposition.posPart.HaveLebesgueDecomposition μ ∨
¬s.toJordanDecomposition.negPart.HaveLebesgueDecomposition μ- Cited by
- 0 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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 and proof · cited by 10,939
- MeasureTheory.SignedMeasurestatement and proof · cited by 108
- MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
- not_and_orproof · cited by 82
- MeasureTheory.JordanDecomposition.negPartstatement and proof · cited by 44
- MeasureTheory.JordanDecomposition.posPartstatement and proof · cited by 43
- MeasureTheory.SignedMeasure.toJordanDecompositionstatement and proof · cited by 34
- MeasureTheory.SignedMeasure.HaveLebesgueDecompositionstatement and proof · cited by 10
- not_or_of_impproof · cited by 8
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