Theorems · Theorem · measure theory
MeasureTheory.SignedMeasure.haveLebesgueDecomposition_mk
∀ {α : Type u_1} {m : MeasurableSpace α} {s t : MeasureTheory.SignedMeasure α} (μ : MeasureTheory.Measure α)
{f : α → ℝ},
Measurable f →
MeasureTheory.VectorMeasure.MutuallySingular t μ.toENNRealVectorMeasure →
s = t + μ.withDensityᵥ f → s.HaveLebesgueDecomposition μ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 264 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- add_zeroproof · cited by 2,707
- Measurablestatement and proof · cited by 1,499
- MeasureTheory.Integrableproof · cited by 1,367
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
- MeasureTheory.SignedMeasurestatement and proof · cited by 108
- MeasureTheory.Measure.withDensityᵥstatement and proof · cited by 36
- MeasureTheory.integrable_zeroproof · cited by 22
- MeasureTheory.VectorMeasure.MutuallySingularstatement and proof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.SignedMeasure.eq_rnDerivproof · cited by 0