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Theorems · Definition · measure theory

MeasureTheory.Content.measure

{G : Type w} →
  [inst : TopologicalSpace G] →
    MeasureTheory.Content G → [R1Space G] → [S : MeasurableSpace G] → [BorelSpace G] → MeasureTheory.Measure G

The measure induced by the outer measure coming from a content, on the Borel sigma-algebra.

Defined in
Mathlib.MeasureTheory.Measure.Content
Cited by
10 results in Mathlib
Foundations
Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceR1SpaceMeasurableSpaceBorelSpace

Around this declaration

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

MeasureTheory.Measure.addHaarMeasure · cited by 21Measure.addHaarMeasureMeasureTheory.Measure.haarMeasure · cited by 10Measure.haarMeasureRealRMK.rieszMeasure · cited by 8RealRMK.rieszMeasureNNRealRMK.rieszMeasure · cited by 7NNRealRMK.rieszMeasureMeasureTheory.Content.measure_apply · cited by 6Content.measure_applyMeasureTheory.Measure.addHaarMeasure_self · cited by 6Measure.addHaarMeasure_se…MeasureTheory.Measure.haarMeasure_self · cited by 4Measure.haarMeasure_selfMeasureTheory.Content.measure_eq_content_of_regular · cited by 3Content.measure_eq_conten…NNRealRMK.integral_rieszMeasure · cited by 3NNRealRMK.integral_rieszM…MeasureTheory.Content.measure.congr_simp · cited by 1measure.congr_simpRealRMK.exists_open_approx · cited by 0RealRMK.exists_open_approxMeasureTheory.Measure.addHaarMeasure_apply · cited by 0Measure.addHaarMeasure_ap…RealRMK.le_rieszMeasure_tsupport_subset · cited by 0RealRMK.le_rieszMeasure_t…MeasureTheory.Measure.haarMeasure_apply · cited by 0Measure.haarMeasure_applyTopologicalSpace · cited by 24529TopologicalSpaceMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureBorelSpace · cited by 1602BorelSpaceR1Space · cited by 125R1SpaceMeasureTheory.Content · cited by 60MeasureTheory.ContentMeasureTheory.Content.outerMeasure · cited by 24Content.outerMeasureMeasureTheory.OuterMeasure.toMeasure · cited by 11OuterMeasure.toMeasureMeasureTheory.Content.borel_le_caratheodory · cited by 1Content.borel_le_caratheo…Content.measureCITED BYCITES

Cites9

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

Cited by14

Results whose statement or proof uses this declaration.