Theorems · Definition · measure theory
MeasureTheory.ComplexMeasure.singularPart
{α : Type u_1} →
{m : MeasurableSpace α} → MeasureTheory.ComplexMeasure α → MeasureTheory.Measure α → MeasureTheory.ComplexMeasure αThe singular part between a complex measure c and a positive measure μ is the complex
measure satisfying c.singularPart μ + μ.withDensityᵥ (c.rnDeriv μ) = c. This property is given
by MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.SignedMeasure.singularPartproof · cited by 13
- MeasureTheory.ComplexMeasurestatement and proof · cited by 13
- MeasureTheory.SignedMeasure.toComplexMeasureproof · cited by 8
- MeasureTheory.ComplexMeasure.improof · cited by 7
- MeasureTheory.ComplexMeasure.reproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eqstatement and proof · cited by 0