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Theorems · Theorem · measure theory

IsClosed.measurableSet

∀ {α : Type u_1} {s : Set α} [inst : TopologicalSpace α] [inst_1 : MeasurableSpace α] [OpensMeasurableSpace α],
  IsClosed s → MeasurableSet s
Defined in
Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
Cited by
65 results in Mathlib
Foundations
Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceMeasurableSpaceOpensMeasurableSpace

Around this declaration

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

measurableSet_Icc · cited by 32measurableSet_IccmeasurableSet_Ici · cited by 26measurableSet_IciIsCompact.measurableSet · cited by 25IsCompact.measurableSetmeasurableSet_Iic · cited by 23measurableSet_IicContinuous.integrable_of_hasCompactSupport · cited by 18Continuous.integrable_of_…Topology.IsClosedEmbedding.measurableEmbedding · cited by 16IsClosedEmbedding.measura…measurableSet_closedBall · cited by 13measurableSet_closedBallMeasureTheory.StronglyMeasurable.measurableSet_le · cited by 9StronglyMeasurable.measur…IsClosed.nullMeasurableSet · cited by 8IsClosed.nullMeasurableSetMeasureTheory.Measure.addHaarMeasure_self · cited by 6Measure.addHaarMeasure_se…measurableSet_closure · cited by 6measurableSet_closureMeasureTheory.integral_mono_measure · cited by 5MeasureTheory.integral_mo…exists_partition_approximatesLinearOn_of_hasFDerivWithinAt · cited by 5exists_partition_approxim…MeasureTheory.MemLp.isProbabilityMeasure_of_indepFun · cited by 5MemLp.isProbabilityMeasur…MeasureTheory.Measure.measure_isAddInvariant_eq_smul_of_isCompact_closure · cited by 4Measure.measure_isAddInva…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasurableSet · cited by 3075MeasurableSetIsClosed · cited by 1639IsClosedOpensMeasurableSpace · cited by 636OpensMeasurableSpaceIsClosed.isOpen_compl · cited by 126IsClosed.isOpen_complIsOpen.measurableSet · cited by 82IsOpen.measurableSetMeasurableSet.of_compl · cited by 11MeasurableSet.of_complIsClosed.measurableSetCITED BYCITES

Cites9

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.