Loogle!

Result

Found 18 declarations mentioning PMF.map.

• PMF.map 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} (f : α → β) (p : PMF α) : PMF β
• PMF.map_id 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} (p : PMF α) : PMF.map id p = p
• PMF.map_const 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} (p : PMF α) (b : β) : PMF.map (Function.const α b) p = PMF.pure b
• PMF.pure_map 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} (f : α → β) (a : α) : PMF.map f (PMF.pure a) = PMF.pure (f a)
• PMF.support_map 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} (f : α → β) (p : PMF α) : (PMF.map f p).support = f '' p.support
• PMF.monad_map_eq_map 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α β : Type u} (f : α → β) (p : PMF α) : f <$> p = PMF.map f p
• PMF.bind_pure_comp 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} (f : α → β) (p : PMF α) : p.bind (PMF.pure ∘ f) = PMF.map f p
• PMF.map.eq_1 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} (f : α → β) (p : PMF α) : PMF.map f p = p.bind (PMF.pure ∘ f)
• PMF.map_comp 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} (f : α → β) (p : PMF α) (g : β → γ) : PMF.map g (PMF.map f p) = PMF.map (g ∘ f) p
• PMF.bind_map 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} (p : PMF α) (f : α → β) (q : β → PMF γ) : (PMF.map f p).bind q = p.bind (q ∘ f)
• PMF.map_bind 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} (p : PMF α) (q : α → PMF β) (f : β → γ) : PMF.map f (p.bind q) = p.bind fun a => PMF.map f (q a)
• PMF.toMeasure_map 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} (f : α → β) {mα : MeasurableSpace α} {mβ : MeasurableSpace β} (p : PMF α) (hf : Measurable f) : MeasureTheory.Measure.map f p.toMeasure = (PMF.map f p).toMeasure
• PMF.mem_support_map_iff 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} (f : α → β) (p : PMF α) (b : β) : b ∈ (PMF.map f p).support ↔ ∃ a ∈ p.support, f a = b
• PMF.toOuterMeasure_map_apply 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} (f : α → β) (p : PMF α) (s : Set β) : (PMF.map f p).toOuterMeasure s = p.toOuterMeasure (f ⁻¹' s)
• PMF.map_apply 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} (f : α → β) (p : PMF α) (b : β) : (PMF.map f p) b = ∑' (a : α), if b = f a then p a else 0
• PMF.toMeasure_map_apply 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} (f : α → β) (p : PMF α) (s : Set β) {mα : MeasurableSpace α} {mβ : MeasurableSpace β} (hf : Measurable f) (hs : MeasurableSet s) : (PMF.map f p).toMeasure s = p.toMeasure (f ⁻¹' s)
• PMF.map_ofFintype 📋 Mathlib.Probability.ProbabilityMassFunction.Constructions
  {α : Type u_1} {β : Type u_2} [Fintype α] [Fintype β] (f : α → ENNReal) (h : ∑ a, f a = 1) (g : α → β) : PMF.map g (PMF.ofFintype f h) = PMF.ofFintype (fun b => ∑ a with g a = b, f a) ⋯
• PMF.binomial_one_eq_bernoulli 📋 Mathlib.Probability.ProbabilityMassFunction.Binomial
  (p : ENNReal) (h : p ≤ 1) : PMF.binomial p h 1 = PMF.map (fun x => bif x then 1 else 0) (PMF.bernoulli p h)

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. By subexpression:
   🔍 _ * (_ ^ _)
   finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

   The pattern can also be non-linear, as in
   🔍 Real.sqrt ?a * Real.sqrt ?a

   If the pattern has parameters, they are matched in any order. Both of these will find List.map:
   🔍 (?a -> ?b) -> List ?a -> List ?b
   🔍 List ?a -> (?a -> ?b) -> List ?b

4. By main conclusion:
   🔍 |- tsum _ = _ * tsum _
   finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

   As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
   🔍 |- _ < _ → tsum _ < tsum _
   will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

The #lucky button will directly send you to the documentation of the first hit.

Source code

You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO.

This is Loogle revision 19971e9 serving mathlib revision 40fea08