Theorems · Theorem · measure theory
MeasureTheory.Measure.singularPart_def
∀ {α : Type u_2} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α),
μ.singularPart ν = if h : μ.HaveLebesgueDecomposition ν then (Classical.choose ⋯).1 else 0- Cited by
- 5 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- ENNRealstatement · cited by 9,879
- Measurablestatement · cited by 1,499
- MeasureTheory.Measure.withDensitystatement · cited by 265
- MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
- MeasureTheory.Measure.MutuallySingularstatement · cited by 91
- MeasureTheory.Measure.singularPartstatement · cited by 71
- MeasureTheory.Measure.HaveLebesgueDecomposition.lebesgue_decompositionstatement and proof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.singularPart_leproof · cited by 7
- MeasureTheory.Measure.haveLebesgueDecomposition_specproof · cited by 6
- MeasureTheory.Measure.singularPart_smulproof · cited by 4
- MeasureTheory.Measure.singularPart_smul_rightproof · cited by 2
- MeasureTheory.Measure.singularPart_of_not_haveLebesgueDecompositionproof · cited by 1