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Theorems · Theorem · measure theory

measurableSet_Iic

∀ {α : Type u_1} [inst : TopologicalSpace α] {mα : MeasurableSpace α} [OpensMeasurableSpace α] [inst_2 : Preorder α]
  {a : α} [ClosedIicTopology α], MeasurableSet (Set.Iic a)
Defined in
Mathlib.MeasureTheory.Constructions.BorelSpace.Order
Cited by
23 results in Mathlib
Foundations
Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceOpensMeasurableSpacePreorderClosedIicTopology

Around this declaration

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

measurableSet_Ioc · cited by 65measurableSet_IocintervalIntegral.continuousWithinAt_primitive · cited by 6intervalIntegral.continuo…MeasureTheory.Measure.IicSnd_apply · cited by 5Measure.IicSnd_applyMeasureTheory.norm_setIntegral_le_of_norm_le_const_ae' · cited by 3MeasureTheory.norm_setInt…nullMeasurableSet_Iic · cited by 2nullMeasurableSet_IicProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat · cited by 2ProbabilityTheory.setLInt…ProbabilityTheory.setLIntegral_toKernel_univ · cited by 2ProbabilityTheory.setLInt…integral_comp_abs · cited by 2integral_comp_absMeasureTheory.Measure.iInf_rat_gt_prod_Iic · cited by 2Measure.iInf_rat_gt_prod_…MeasureTheory.StronglyAdapted.isStoppingTime_crossing · cited by 2StronglyAdapted.isStoppin…intervalIntegral.integral_indicator · cited by 1intervalIntegral.integral…ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_real · cited by 1ProbabilityTheory.eq_cond…ProbabilityTheory.lintegral_betaPDF · cited by 1ProbabilityTheory.lintegr…ProbabilityTheory.lintegral_exponentialPDF_eq_antiDeriv · cited by 1ProbabilityTheory.lintegr…NumberField.mixedEmbedding.fundamentalCone.measurableSet_paramSet · cited by 1fundamentalCone.measurabl…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpacePreorder · cited by 7952PreorderMeasurableSet · cited by 3075MeasurableSetSet.Iic · cited by 1111Set.IicOpensMeasurableSpace · cited by 636OpensMeasurableSpaceClosedIicTopology · cited by 115ClosedIicTopologyIsClosed.measurableSet · cited by 65IsClosed.measurableSetisClosed_Iic · cited by 23isClosed_IicmeasurableSet_IicCITED BYCITES

Cites9

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Cited by23

Results whose statement or proof uses this declaration.