Mathlib Map

Theorems · Theorem · measure theory

measurableSet_Icc

∀ {α : Type u_1} [inst : TopologicalSpace α] {mα : MeasurableSpace α} [OpensMeasurableSpace α] [inst_2 : Preorder α]
  {a b : α} [OrderClosedTopology α], MeasurableSet (Set.Icc a b)
Defined in
Mathlib.MeasureTheory.Constructions.BorelSpace.Order
Cited by
32 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceOpensMeasurableSpacePreorderOrderClosedTopology

Around this declaration

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

BoundedVariationOn.vectorMeasure_Icc · cited by 6BoundedVariationOn.vector…intervalIntegral.integral_deriv_smul_comp''' · cited by 4intervalIntegral.integral…ODE.hasDerivWithinAt_picard_Icc · cited by 3ODE.hasDerivWithinAt_pica…MeasureTheory.aecover_Ioo_of_Icc · cited by 3MeasureTheory.aecover_Ioo…intervalIntegral.integral_nonneg · cited by 3intervalIntegral.integral…integrableOn_mul_sum_Icc · cited by 3integrableOn_mul_sum_IccnullMeasurableSet_Icc · cited by 2nullMeasurableSet_IccProbabilityTheory.BrownianReal.posSemidef_covMatrix · cited by 2BrownianReal.posSemidef_c…BoundedVariationOn.vectorMeasure_Ici · cited by 2BoundedVariationOn.vector…BoxIntegral.Box.measurableSet_Icc · cited by 2Box.measurableSet_IccManifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc · cited by 2Manifold.lintegral_norm_m…setOfPred_riemannianEDist_lt_subset_nhds · cited by 2setOfPred_riemannianEDist…Manifold.pathELength_comp_of_monotoneOn · cited by 2Manifold.pathELength_comp…eventually_riemannianEDist_le_edist_extChartAt · cited by 1eventually_riemannianEDis…BoundedVariationOn.vectorMeasure_Iic · cited by 1BoundedVariationOn.vector…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpacePreorder · cited by 7952PreorderMeasurableSet · cited by 3075MeasurableSetSet.Icc · cited by 1702Set.IccOpensMeasurableSpace · cited by 636OpensMeasurableSpaceOrderClosedTopology · cited by 445OrderClosedTopologyIsClosed.measurableSet · cited by 65IsClosed.measurableSetisClosed_Icc · cited by 17isClosed_IccmeasurableSet_IccCITED BYCITES

Cites9

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

Cited by32

Results whose statement or proof uses this declaration.