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Theorems · Theorem · measure theory

MeasureTheory.ae.congr_simp

∀ {α : Type u_1} {F : Type u_3} [inst : FunLike F (Set α) ENNReal] [inst_1 : MeasureTheory.OuterMeasureClass F α]
  (μ μ_1 : F), μ = μ_1 → MeasureTheory.ae μ = MeasureTheory.ae μ_1
Defined in
Mathlib.MeasureTheory.OuterMeasure.AE
Cited by
39 results in Mathlib
Foundations
Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FunLikeMeasureTheory.OuterMeasureClass

Around this declaration

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

MeasureTheory.Measure.rnDeriv_eq_zero_of_mutuallySingular · cited by 5Measure.rnDeriv_eq_zero_o…intervalIntegral.integral_deriv_of_contDiffOn_Icc · cited by 4intervalIntegral.integral…ProbabilityTheory.condDistrib_ae_eq_of_measure_eq_compProd · cited by 4ProbabilityTheory.condDis…MeasureTheory.ae_toFinite · cited by 3MeasureTheory.ae_toFiniteMeasureTheory.condExp_stronglyMeasurable_bilin_of_bound · cited by 3MeasureTheory.condExp_str…MeasureTheory.toReal_rnDeriv_trim · cited by 3MeasureTheory.toReal_rnDe…MeasureTheory.setToFun_measure_zero · cited by 3MeasureTheory.setToFun_me…MeasureTheory.ae_restrict_of_ae_eq_of_ae_restrict · cited by 2MeasureTheory.ae_restrict…MeasureTheory.ae_restrict_union_eq · cited by 2MeasureTheory.ae_restrict…ProbabilityTheory.Kernel.ae_compProd_of_ae_ae · cited by 2Kernel.ae_compProd_of_ae_…ProbabilityTheory.condDistrib_comp_self · cited by 2ProbabilityTheory.condDis…MeasureTheory.AEMeasurable.ae_eq_of_forall_setLIntegral_eq · cited by 2AEMeasurable.ae_eq_of_for…MeasureTheory.Martingale.stoppedValue_ae_eq_condExp_of_le_const_of_countable_range · cited by 2Martingale.stoppedValue_a…MeasureTheory.llr_tilted_left · cited by 2MeasureTheory.llr_tilted_…MeasureTheory.llr_tilted_right · cited by 2MeasureTheory.llr_tilted_…Set · cited by 53352SetENNReal · cited by 9879ENNRealFilter · cited by 8121FilterFunLike · cited by 2560FunLikeMeasureTheory.ae · cited by 2352MeasureTheory.aeMeasureTheory.OuterMeasureClass · cited by 104MeasureTheory.OuterMeasur…ae.congr_simpCITED BYCITES

Cites6

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Cited by39

Results whose statement or proof uses this declaration.