Theorems · Theorem · measure theory

MeasureTheory.withDensity_ofReal_mutuallySingular

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {f : α → ℝ},
  Measurable f →
    (μ.withDensity fun x => ENNReal.ofReal (f x)).MutuallySingular (μ.withDensity fun x => ENNReal.ofReal (-f x))

Defined in: Mathlib.MeasureTheory.Measure.WithDensity
Cited by: 1 results in Mathlib
Foundations: Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

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

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Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.SignedMeasure.jordanDecomposition_add_withDensity_mutuallySingularproof · cited by 1