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Theorems · Definition · measure theory

MeasureTheory.AddContent.measureCaratheodory

{α : Type u_1} →
  {C : Set (Set α)} →
    (m : MeasureTheory.AddContent ENNReal C) →
      (hC : MeasureTheory.IsSetSemiring C) → m.IsSigmaSubadditive → MeasureTheory.Measure α

Construct a measure from a sigma-subadditive content on a semiring. This measure is defined on the associated Carathéodory sigma-algebra.

Defined in
Mathlib.MeasureTheory.OuterMeasure.OfAddContent
Cited by
2 results in Mathlib
Foundations
Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
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MeasureTheory.AddContent.measure · cited by 2AddContent.measureMeasureTheory.AddContent.measureCaratheodory_eq · cited by 1AddContent.measureCarathe…MeasureTheory.AddContent.measureCaratheodory_eq_inducedOuterMeasure · cited by 0AddContent.measureCarathe…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealMeasureTheory.OuterMeasure · cited by 287MeasureTheory.OuterMeasureMeasureTheory.IsSetSemiring · cited by 78MeasureTheory.IsSetSemiri…MeasureTheory.AddContent · cited by 78MeasureTheory.AddContentMeasureTheory.OuterMeasure.caratheodory · cited by 37OuterMeasure.caratheodoryMeasureTheory.inducedOuterMeasure · cited by 22MeasureTheory.inducedOute…MeasureTheory.AddContent.IsSigmaSubadditive · cited by 11AddContent.IsSigmaSubaddi…MeasureTheory.addContent_empty · cited by 10MeasureTheory.addContent_…MeasureTheory.IsSetSemiring.empty_mem · cited by 8IsSetSemiring.empty_memAddContent.measureCaratheodoryCITED BYCITES

Cites12

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Cited by3

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