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Theorems · Definition · measure theory

MeasureTheory.Measure.toSignedMeasure

{α : Type u_1} →
  {m : MeasurableSpace α} →
    (μ : MeasureTheory.Measure α) → [hμ : MeasureTheory.IsFiniteMeasure μ] → MeasureTheory.SignedMeasure α

A finite measure coerced into a real function is a signed measure.

Defined in
Mathlib.MeasureTheory.VectorMeasure.Basic
Cited by
36 results in Mathlib
Foundations
Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasureTheory.IsFiniteMeasure
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.SignedMeasure.singularPart · cited by 13SignedMeasure.singularPartMeasureTheory.JordanDecomposition.toSignedMeasure · cited by 13JordanDecomposition.toSig…MeasureTheory.Measure.toSignedMeasure_apply_measurable · cited by 11Measure.toSignedMeasure_a…MeasureTheory.Measure.toSignedMeasure_sub_apply · cited by 6Measure.toSignedMeasure_s…MeasureTheory.SignedMeasure.singularPart_add_withDensity_rnDeriv_eq · cited by 6SignedMeasure.singularPar…MeasureTheory.SignedMeasure.null_of_totalVariation_zero · cited by 3SignedMeasure.null_of_tot…MeasureTheory.Measure.toSignedMeasure.congr_simp · cited by 3toSignedMeasure.congr_simpMeasureTheory.Measure.toSignedMeasure_add · cited by 2Measure.toSignedMeasure_a…MeasureTheory.Measure.toSignedMeasure_restrict_eq_restrict_toSignedMeasure · cited by 2Measure.toSignedMeasure_r…MeasureTheory.Measure.toSignedMeasure_smul · cited by 2Measure.toSignedMeasure_s…MeasureTheory.SignedMeasure.singularPart_neg · cited by 2SignedMeasure.singularPar…MeasureTheory.Measure.variation_toSignedMeasure · cited by 2Measure.variation_toSigne…MeasureTheory.SignedMeasure.withDensityᵥ_rnDeriv_eq · cited by 2SignedMeasure.withDensity…MeasureTheory.VectorMeasure.restrict_toSignedMeasure · cited by 1VectorMeasure.restrict_to…MeasureTheory.Measure.toSignedMeasure_congr · cited by 1Measure.toSignedMeasure_c…Set · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasurableSet · cited by 3075MeasurableSetDisjoint · cited by 2201DisjointMeasureTheory.IsFiniteMeasure · cited by 1078MeasureTheory.IsFiniteMea…Function.onFun · cited by 570Function.onFunMeasureTheory.Measure.real · cited by 530Measure.realPairwise · cited by 516PairwiseMeasureTheory.SignedMeasure · cited by 108MeasureTheory.SignedMeasu…Measure.toSignedMeasureCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by38

Results whose statement or proof uses this declaration.