Theorems · Definition · measure theory
MeasureTheory.OuterMeasure.caratheodory
- 1000+ list: Carathéodory's theorem (measure theory)
{α : Type u} → MeasureTheory.OuterMeasure α → MeasurableSpace αGiven an outer measure μ, the Carathéodory-measurable space is
defined such that s is measurable if ∀ t, μ t = μ (t ∩ s) + μ (t \ s).
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- MeasurableSpacestatement · cited by 13,106
- MeasureTheory.OuterMeasurestatement and proof · cited by 287
- MeasurableSpace.DynkinSystem.toMeasurableSpaceproof · cited by 2
- MeasureTheory.OuterMeasure.isCaratheodory_interproof · cited by 1
- MeasureTheory.OuterMeasure.caratheodoryDynkinproof · cited by 0
Cited by40
Results whose statement or proof uses this declaration.
- MeasureTheory.OuterMeasure.toMeasurestatement and proof · cited by 11
- MeasureTheory.toMeasure_applystatement and proof · cited by 10
- MeasureTheory.le_toMeasure_applystatement and proof · cited by 8
- MeasureTheory.Measure.liftLinearstatement and proof · cited by 5
- MeasureTheory.OuterMeasure.isCaratheodory_iff_lestatement · cited by 4
- MeasureTheory.Measure.pi_caratheodorystatement · cited by 3
- MeasureTheory.OuterMeasure.toMeasure_zerostatement and proof · cited by 3
- MeasureTheory.OuterMeasure.boundedBy_caratheodorystatement · cited by 2
- MeasureTheory.OuterMeasure.ofFunction_caratheodorystatement · cited by 2
- MeasureTheory.toMeasure_apply₀statement and proof · cited by 2
- MeasureTheory.Measure.liftLinear_applystatement and proof · cited by 2
- MeasureTheory.Measure.liftLinear_apply₀statement and proof · cited by 2