Theorems · Inductive type · measure theory
MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition
{α : Type u_1} → {m : MeasurableSpace α} → MeasureTheory.ComplexMeasure α → MeasureTheory.Measure α → PropA complex measure is said to HaveLebesgueDecomposition with respect to a positive measure
if both its real and imaginary part HaveLebesgueDecomposition with respect to that measure.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- MeasureTheory.ComplexMeasurestatement · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.casesOnstatement and proof · cited by 0
- MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.recOnstatement and proof · cited by 0
- MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eqstatement and proof · cited by 0