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Theorems · Theorem · measure theory

MeasurableEmbedding.mutuallySingular_map

∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} {β : Type u_2} {x : MeasurableSpace β}
  {f : α → β},
  MeasurableEmbedding f →
    μ.MutuallySingular ν → (MeasureTheory.Measure.map f μ).MutuallySingular (MeasureTheory.Measure.map f ν)
Defined in
Mathlib.MeasureTheory.Measure.MutuallySingular
Cited by
2 results in Mathlib
Foundations
Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
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MeasurableEmbedding.rnDeriv_map · cited by 1MeasurableEmbedding.rnDer…MeasurableEmbedding.singularPart_map · cited by 0MeasurableEmbedding.singu…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealSet.image · cited by 5609Set.imageCompl.compl · cited by 2925Compl.complMeasureTheory.Measure.map · cited by 858Measure.mapMeasurableEmbedding · cited by 170MeasurableEmbeddingMeasureTheory.Measure.MutuallySingular · cited by 91Measure.MutuallySingularSet.preimage_compl · cited by 43Set.preimage_complMeasurableEmbedding.injective · cited by 35MeasurableEmbedding.injec…Function.Injective.preimage_image · cited by 30Injective.preimage_imageMeasurableEmbedding.map_apply · cited by 16MeasurableEmbedding.map_a…MeasureTheory.Measure.MutuallySingular.nullSet · cited by 16MutuallySingular.nullSetMeasurableEmbedding.mutuallyS…CITED BYCITES

Cites19

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Cited by2

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