Theorems · Theorem · measure theory
MeasureTheory.ComplexMeasure.im_apply
∀ {α : Type u_1} {m : MeasurableSpace α} (v : MeasureTheory.VectorMeasure α ℂ),
MeasureTheory.ComplexMeasure.im v = v.mapRange Complex.imLm.toAddMonoidHom Complex.continuous_im- Defined in
- Mathlib.MeasureTheory.Measure.Complex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- MeasurableSpacestatement and proof · cited by 13,106
- LinearMapstatement · cited by 10,215
- Complexstatement and proof · cited by 5,565
- MeasureTheory.VectorMeasurestatement and proof · cited by 451
- MeasureTheory.SignedMeasurestatement · cited by 108
- LinearMap.toAddMonoidHomstatement · cited by 101
- Complex.continuous_imstatement · cited by 32
- MeasureTheory.VectorMeasure.mapRangestatement · cited by 24
- MeasureTheory.ComplexMeasurestatement · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iffproof · cited by 0