Theorems · Definition · measure theory
MeasureTheory.ComplexMeasure.im
{α : Type u_1} → {m : MeasurableSpace α} → MeasureTheory.ComplexMeasure α →ₗ[ℝ] MeasureTheory.SignedMeasure αThe imaginary part of a complex measure is a signed measure.
- Defined in
- Mathlib.MeasureTheory.Measure.Complex
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- MeasurableSpacestatement and proof · cited by 13,106
- LinearMapstatement · cited by 10,215
- Complexstatement · cited by 5,565
- ContinuousLinearMap.toLinearMapproof · cited by 528
- MeasureTheory.SignedMeasurestatement · cited by 108
- Complex.continuous_improof · cited by 32
- Complex.imCLMproof · cited by 17
- MeasureTheory.ComplexMeasurestatement · cited by 13
- MeasureTheory.VectorMeasure.mapRangeₗproof · cited by 0
Cited by12
Results whose statement or proof uses this declaration.
- MeasureTheory.ComplexMeasure.equivSignedMeasureproof · cited by 4
- MeasureTheory.ComplexMeasure.rnDerivproof · cited by 2
- MeasureTheory.ComplexMeasure.im_applystatement and proof · cited by 1
- MeasureTheory.ComplexMeasure.integrable_rnDerivproof · cited by 1
- MeasureTheory.ComplexMeasure.singularPartproof · cited by 1
- MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasurestatement · cited by 1
- MeasureTheory.SignedMeasure.im_toComplexMeasurestatement · cited by 0
- MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.casesOnstatement and proof · cited by 0
- MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.recOnstatement and proof · cited by 0
- MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iffstatement and proof · cited by 0
- MeasureTheory.ComplexMeasure.equivSignedMeasure_applystatement · cited by 0
- MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eqproof · cited by 0