Theorems · Theorem · probability
ProbabilityTheory.cond_add_cond_compl_eq
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {s t : Set Ω},
MeasurableSet s →
∀ (μ : MeasureTheory.Measure Ω) [MeasureTheory.IsFiniteMeasure μ], μ[t | s] * μ s + μ[t | sᶜ] * μ sᶜ = μ tA version of the law of total probability.
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- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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
- Compl.complstatement and proof · cited by 2,925
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- Set.inter_commproof · cited by 291
- MeasurableSet.complproof · cited by 172
- ProbabilityTheory.condstatement and proof · cited by 43
- MeasureTheory.measure_inter_add_sdiffproof · cited by 16
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