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Theorems · Theorem · measure theory

MeasureTheory.Measure.AbsolutelyContinuous.trans

∀ {α : Type u_1} {mα : MeasurableSpace α} {μ₁ μ₂ μ₃ : MeasureTheory.Measure α},
  μ₁.AbsolutelyContinuous μ₂ → μ₂.AbsolutelyContinuous μ₃ → μ₁.AbsolutelyContinuous μ₃
Defined in
Mathlib.MeasureTheory.Measure.AbsolutelyContinuous
Cited by
17 results in Mathlib
Foundations
Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

MeasureTheory.Measure.QuasiMeasurePreserving.comp · cited by 21QuasiMeasurePreserving.co…MeasureTheory.Measure.rnDeriv_eq_zero_of_mutuallySingular · cited by 5Measure.rnDeriv_eq_zero_o…MeasureTheory.Measure.singularPart_eq_zero_of_ac · cited by 4Measure.singularPart_eq_z…MeasureTheory.Measure.absolutelyContinuous_of_le_smul · cited by 3Measure.absolutelyContinu…MeasureTheory.Measure.AbsolutelyContinuous.add_left_iff · cited by 3AbsolutelyContinuous.add_…MeasureTheory.Measure.AbsolutelyContinuous.smul_right · cited by 2AbsolutelyContinuous.smul…MeasureTheory.Measure.QuasiMeasurePreserving.mono_left · cited by 2QuasiMeasurePreserving.mo…MeasureTheory.Measure.AbsolutelyContinuous.compProd · cited by 1AbsolutelyContinuous.comp…MeasureTheory.IsFundamentalDomain.measure_eq_tsum_of_ac · cited by 1IsFundamentalDomain.measu…ProbabilityTheory.cond_absolutelyContinuous · cited by 1ProbabilityTheory.cond_ab…MeasureTheory.Measure.absolutelyContinuous_compProd_of_compProd · cited by 1Measure.absolutelyContinu…MeasureTheory.Measure.QuasiMeasurePreserving.mono_right · cited by 1QuasiMeasurePreserving.mo…MeasureTheory.pdf.quasiMeasurePreserving_hasPDF · cited by 1pdf.quasiMeasurePreservin…MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum_of_ac · cited by 1IsAddFundamentalDomain.me…InformationTheory.integral_llr_add_mul_log_nonneg · cited by 0InformationTheory.integra…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.Measure.AbsolutelyContinuous · cited by 325Measure.AbsolutelyContinu…AbsolutelyContinuous.transCITED BYCITES

Cites5

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

Cited by17

Results whose statement or proof uses this declaration.