Theorems · Theorem · measure theory
MeasureTheory.Measure.toSignedMeasure_apply_measurable
∀ {α : Type u_1} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : MeasureTheory.IsFiniteMeasure μ]
{i : Set α}, MeasurableSet i → μ.toSignedMeasure i = μ.real i- Cited by
- 11 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.Measure.realstatement · cited by 530
- MeasureTheory.SignedMeasurestatement · cited by 108
- MeasureTheory.Measure.toSignedMeasurestatement · cited by 36
Cited by11
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.toSignedMeasure_sub_applyproof · cited by 6
- MeasureTheory.Measure.toSignedMeasure_addproof · cited by 2
- MeasureTheory.Measure.toSignedMeasure_smulproof · cited by 2
- MeasureTheory.SignedMeasure.withDensityᵥ_rnDeriv_eqproof · cited by 2
- MeasureTheory.VectorMeasure.integral_toSignedMeasureproof · cited by 1
- MeasureTheory.VectorMeasure.restrict_toSignedMeasureproof · cited by 1
- MeasureTheory.withDensityᵥ_toRealproof · cited by 1
- MeasureTheory.Measure.toSignedMeasure_eq_toSignedMeasure_iffproof · cited by 0
- MeasureTheory.Measure.toSignedMeasure_le_toSignedMeasure_iffproof · cited by 0