Theorems · Theorem · probability
ProbabilityTheory.iIndepSet.isProbabilityMeasure
∀ {Ω : Type u_1} {ι : Type u_2} {x : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {s : ι → Set Ω},
ProbabilityTheory.iIndepSet s μ → MeasureTheory.IsProbabilityMeasure μ- Defined in
- Mathlib.Probability.Independence.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.IsProbabilityMeasurestatement · cited by 392
- ProbabilityTheory.iIndepSetstatement and proof · cited by 19
- ProbabilityTheory.iIndepSet_iff_iIndepproof · cited by 1
- ProbabilityTheory.iIndep.isProbabilityMeasureproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.measure_limsup_eq_oneproof · cited by 0