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Theorems · Definition · measure theory

MeasureTheory.OuterMeasure.trim

{α : Type u_1} → [MeasurableSpace α] → MeasureTheory.OuterMeasure α → MeasureTheory.OuterMeasure α

Given an outer measure m we can forget its value on non-measurable sets, and then consider m.trim, the unique maximal outer measure less than that function.

Defined in
Mathlib.MeasureTheory.OuterMeasure.Induced
Cited by
40 results in Mathlib
Foundations
Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpace

Around this declaration

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

MeasureTheory.OuterMeasure.trim_eq · cited by 8OuterMeasure.trim_eqMeasureTheory.Measure.trimmed · cited by 6Measure.trimmedMeasureTheory.OuterMeasure.trim_eq_iInf · cited by 6OuterMeasure.trim_eq_iInfMeasureTheory.OuterMeasure.le_trim · cited by 6OuterMeasure.le_trimMeasureTheory.OuterMeasure.exists_measurable_superset_eq_trim · cited by 4OuterMeasure.exists_measu…MeasureTheory.OuterMeasure.le_trim_iff · cited by 4OuterMeasure.le_trim_iffMeasureTheory.OuterMeasure.exists_measurable_superset_forall_eq_trim · cited by 3OuterMeasure.exists_measu…MeasureTheory.OuterMeasure.trim_binop · cited by 3OuterMeasure.trim_binopMeasureTheory.Measure.toOuterMeasure_injective · cited by 2Measure.toOuterMeasure_in…MeasureTheory.measure_eq_trim · cited by 2MeasureTheory.measure_eq_…MeasureTheory.OuterMeasure.trim_eq_trim_iff · cited by 2OuterMeasure.trim_eq_trim…MeasureTheory.OuterMeasure.restrict_trim · cited by 1OuterMeasure.restrict_trimMeasureTheory.Measure.trim_le · cited by 1Measure.trim_leMeasureTheory.toMeasure_toOuterMeasure · cited by 1MeasureTheory.toMeasure_t…MeasureTheory.OuterMeasure.trim_congr · cited by 1OuterMeasure.trim_congrDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasurableSet · cited by 3075MeasurableSetMeasureTheory.OuterMeasure · cited by 287MeasureTheory.OuterMeasureMeasurableSet.empty · cited by 58MeasurableSet.emptyMeasureTheory.inducedOuterMeasure · cited by 22MeasureTheory.inducedOute…MeasureTheory.OuterMeasure.empty · cited by 5OuterMeasure.emptyOuterMeasure.trimCITED BYCITES

Cites8

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

Cited by45

Results whose statement or proof uses this declaration.