Theorems · Theorem · probability
ProbabilityTheory.cond_eq_inv_mul_cond_mul
- 1000+ list: Bayes' theorem
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {s t : Set Ω},
MeasurableSet s →
MeasurableSet t →
∀ (μ : MeasureTheory.Measure Ω) [MeasureTheory.IsFiniteMeasure μ], μ[t | s] = (μ s)⁻¹ * μ[s | t] * μ tBayes' Theorem
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- mul_assocproof · cited by 1,667
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- Set.inter_commproof · cited by 291
- ProbabilityTheory.condstatement and proof · cited by 43
- ProbabilityTheory.cond_applyproof · cited by 20
- ProbabilityTheory.cond_mul_eq_interproof · cited by 3
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