Mathlib Map

Theorems · Theorem · measure theory

measurableSet_Ioc

∀ {α : Type u_1} [inst : TopologicalSpace α] {mα : MeasurableSpace α} [OpensMeasurableSpace α] [inst_2 : LinearOrder α]
  {a b : α} [ClosedIicTopology α], MeasurableSet (Set.Ioc a b)
Defined in
Mathlib.MeasureTheory.Constructions.BorelSpace.Order
Cited by
65 results in Mathlib
Foundations
Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceOpensMeasurableSpaceLinearOrderClosedIicTopology

Around this declaration

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

measurableSet_uIoc · cited by 20measurableSet_uIocintervalIntegral.integral_congr · cited by 18intervalIntegral.integral…IntervalIntegrable.continuousOn_mul · cited by 8IntervalIntegrable.contin…StieltjesFunction.measure_Icc · cited by 8StieltjesFunction.measure…IntervalIntegrable.mul_continuousOn · cited by 7IntervalIntegrable.mul_co…intervalIntegral.intervalIntegrable_cpow' · cited by 7intervalIntegral.interval…BoundedVariationOn.vectorMeasure_Icc · cited by 6BoundedVariationOn.vector…IntervalIntegrable.continuousOn_smul · cited by 6IntervalIntegrable.contin…intervalIntegral.intervalIntegrable_rpow' · cited by 6intervalIntegral.interval…BoxIntegral.Box.measurableSet_coe · cited by 5Box.measurableSet_coeintervalIntegral.integral_mono_on · cited by 5intervalIntegral.integral…fourierCoeffOn_eq_integral · cited by 5fourierCoeffOn_eq_integralMeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul · cited by 3MeasureTheory.lintegral_c…IntervalIntegrable.smul_continuousOn · cited by 3IntervalIntegrable.smul_c…MeasureTheory.AEStronglyMeasurable.truncation · cited by 3AEStronglyMeasurable.trun…TopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceLinearOrder · cited by 8572LinearOrderMeasurableSet · cited by 3075MeasurableSetSet.Ioc · cited by 971Set.IocOpensMeasurableSpace · cited by 636OpensMeasurableSpaceMeasurableSet.inter · cited by 167MeasurableSet.interClosedIicTopology · cited by 115ClosedIicTopologymeasurableSet_Ioi · cited by 83measurableSet_IoimeasurableSet_Iic · cited by 23measurableSet_IicmeasurableSet_IocCITED BYCITES

Cites10

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

Cited by65

Results whose statement or proof uses this declaration.