Theorems · Theorem · probability
ProbabilityTheory.cond_mul_eq_inter
∀ {Ω : Type u_1} {m : MeasurableSpace Ω} {s : Set Ω},
MeasurableSet s →
∀ (t : Set Ω) (μ : MeasureTheory.Measure Ω) [MeasureTheory.IsFiniteMeasure μ], μ[t | s] * μ s = μ (s ∩ t)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · 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 · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.measure_ne_topproof · cited by 171
- ProbabilityTheory.condstatement · cited by 43
- ProbabilityTheory.cond_mul_eq_inter'proof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- ProbabilityTheory.cond_eq_inv_mul_cond_mulproof · cited by 0
- ProbabilityTheory.cond_add_cond_compl_eqproof · cited by 0
- ProbabilityTheory.sum_meas_smul_cond_fiberproof · cited by 0