Mathlib Map

Theorems · Definition · measure theory

MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub

{X : Type u_1} →
  {mX : MeasurableSpace X} →
    (μ ν : MeasureTheory.Measure X) →
      [MeasureTheory.IsFiniteMeasure μ] → [MeasureTheory.IsFiniteMeasure ν] → MeasureTheory.JordanDecomposition X

The Jordan decomposition associated to the pair of mutually singular measures μ - ν and ν - μ.

Defined in
Mathlib.MeasureTheory.VectorMeasure.Decomposition.JordanSub
Cited by
5 results in Mathlib
Foundations
Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasureTheory.IsFiniteMeasureMeasureTheory.IsFiniteMeasure
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub_toSignedMeasure · cited by 1Measure.jordanDecompositi…MeasureTheory.Measure.toJordanDecomposition_toSignedMeasure_sub · cited by 0Measure.toJordanDecomposi…MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub.congr_simp · cited by 0jordanDecompositionOfToSi…MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub_negPart · cited by 0Measure.jordanDecompositi…MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub_posPart · cited by 0Measure.jordanDecompositi…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.IsFiniteMeasure · cited by 1078MeasureTheory.IsFiniteMea…MeasureTheory.JordanDecomposition · cited by 40MeasureTheory.JordanDecom…MeasureTheory.Measure.mutually_singular_measure_sub · cited by 0Measure.mutually_singular…Measure.jordanDecompositionOf…CITED BYCITES

Cites5

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

Cited by5

Results whose statement or proof uses this declaration.