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 GThe 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
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement · cited by 10,939
- BorelSpacestatement and proof · cited by 1,602
- R1Spacestatement and proof · cited by 125
- MeasureTheory.Contentstatement and proof · cited by 60
- MeasureTheory.Content.outerMeasureproof · cited by 24
- MeasureTheory.OuterMeasure.toMeasureproof · cited by 11
- MeasureTheory.Content.borel_le_caratheodoryproof · cited by 1
Cited by14
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addHaarMeasureproof · cited by 21
- MeasureTheory.Measure.haarMeasureproof · cited by 10
- RealRMK.rieszMeasureproof · cited by 8
- NNRealRMK.rieszMeasureproof · cited by 7
- MeasureTheory.Content.measure_applystatement · cited by 6
- MeasureTheory.Measure.addHaarMeasure_selfproof · cited by 6
- MeasureTheory.Measure.haarMeasure_selfproof · cited by 4
- MeasureTheory.Content.measure_eq_content_of_regularstatement and proof · cited by 3
- NNRealRMK.integral_rieszMeasureproof · cited by 3
- MeasureTheory.Content.measure.congr_simpstatement and proof · cited by 1
- RealRMK.exists_open_approxstatement · cited by 0
- MeasureTheory.Measure.addHaarMeasure_applystatement and proof · cited by 0