Theorems · Theorem · probability
PMF.filter_apply
∀ {α : Type u_1} {p : PMF α} {s : Set α} (h : ∃ a ∈ s, a ∈ p.support) (a : α),
(p.filter s h) a = s.indicator (⇑p) a * (∑' (a' : α), s.indicator (⇑p) a')⁻¹- Cited by
- 1 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- ENNRealstatement and proof · cited by 9,879
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- tsumstatement and proof · cited by 1,148
- Set.indicatorstatement and proof · cited by 723
- PMFstatement and proof · cited by 127
- PMF.supportstatement and proof · cited by 58
- PMF.filterstatement · cited by 6
- PMF.tsum_coe_indicator_ne_topproof · cited by 3
- PMF.normalize_applyproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- PMF.filter_apply_eq_zero_of_notMemproof · cited by 0