Theorems · Definition · probability
ProbabilityTheory.setBernoulli
{ι : Type u_1} → Set ι → ↑unitInterval → MeasureTheory.Measure (Set ι)The product of bernoulli distributions with parameter p on the set u : Set V is the measure
on Set V such that each element of u is taken with probability p, and the elements outside of
u are never taken.
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 279 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.
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- MeasureTheory.Measurestatement · cited by 10,939
- Set.Elemstatement and proof · cited by 7,166
- unitIntervalstatement and proof · cited by 607
- MeasureTheory.Measure.diracproof · cited by 210
- MeasureTheory.Measure.comapproof · cited by 96
- unitInterval.symmproof · cited by 69
- MeasureTheory.Measure.infinitePiproof · cited by 48
- unitInterval.toNNRealproof · cited by 34
Cited by22
Results whose statement or proof uses this declaration.
- ProbabilityTheory.binomialproof · cited by 20
- SimpleGraph.binomialRandomproof · cited by 6
- ProbabilityTheory.setBernoulli_ae_subsetstatement and proof · cited by 5
- ProbabilityTheory.setBernoulli_singletonstatement · cited by 3
- ProbabilityTheory.IsSetBernoulliproof · cited by 2
- ProbabilityTheory.setBernoulli_applystatement · cited by 2
- ProbabilityTheory.setBernoulli_apply_eq_apply_subsetsstatement · cited by 2
- ProbabilityTheory.setBernoulli_emptystatement and proof · cited by 2
- ProbabilityTheory.setBernoulli_eq_mapstatement · cited by 2
- ProbabilityTheory.map_ncard_setBernoulli_real_singletonstatement and proof · cited by 2
- SimpleGraph.binomialRandom_eq_mapstatement · cited by 2
- ProbabilityTheory.setBernoulli_apply'statement · cited by 1