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Theorems · Theorem · measure theory

MeasureTheory.self_mem_ae_restrict

∀ {α : Type u_2} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α},
  MeasurableSet s → s ∈ MeasureTheory.ae (μ.restrict s)
Defined in
Mathlib.MeasureTheory.Measure.Restrict
Cited by
13 results in Mathlib
Foundations
Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

ContinuousOn.aestronglyMeasurable · cited by 21ContinuousOn.aestronglyMe…Real.Gamma_pos_of_pos · cited by 17Real.Gamma_pos_of_posintervalIntegral.integral_deriv_of_contDiffOn_Icc · cited by 4intervalIntegral.integral…integrableOn_peak_smul_of_integrableOn_of_tendsto · cited by 2integrableOn_peak_smul_of…MeasureTheory.lintegral_rpow_eq_lintegral_meas_le_mul · cited by 1MeasureTheory.lintegral_r…MeasureTheory.AEContinuous.hasBoxIntegral · cited by 1AEContinuous.hasBoxIntegr…Real.Gamma_mul_add_mul_le_rpow_Gamma_mul_rpow_Gamma · cited by 1Real.Gamma_mul_add_mul_le…ContinuousOn.aestronglyMeasurable_of_isSeparable · cited by 1ContinuousOn.aestronglyMe…intervalIntegral.integral_derivWithin_Icc_of_contDiffOn_Icc · cited by 1intervalIntegral.integral…enorm_sub_le_lintegral_derivWithin_Icc_of_contDiffOn_Icc · cited by 1enorm_sub_le_lintegral_de…enorm_sub_le_lintegral_deriv_of_contDiffOn_Icc · cited by 1enorm_sub_le_lintegral_de…MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurable_of_sigmaFinite · cited by 1MeasureTheory.lintegral_c…Asymptotics.IsBigO.eventually_integrableOn · cited by 0IsBigO.eventually_integra…Set · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureFilter · cited by 8121FilterSet.univ · cited by 3945Set.univMeasurableSet · cited by 3075MeasurableSetMeasureTheory.ae · cited by 2352MeasureTheory.aeMeasureTheory.Measure.restrict · cited by 1646Measure.restrictSet.univ_inter · cited by 258Set.univ_interSet.Subset.rfl · cited by 255Subset.rflFilter.univ_mem · cited by 96Filter.univ_memMeasureTheory.ae_restrict_eq · cited by 11MeasureTheory.ae_restrict…MeasureTheory.self_mem_ae_res…CITED BYCITES

Cites12

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

Cited by13

Results whose statement or proof uses this declaration.