Loogle!

Result

Found 14 declarations mentioning MeasureTheory.FiniteMeasure.map.

• MeasureTheory.FiniteMeasure.map 📋 Mathlib.MeasureTheory.Measure.FiniteMeasure
  {Ω : Type u_1} {Ω' : Type u_2} [MeasurableSpace Ω] [MeasurableSpace Ω'] (ν : MeasureTheory.FiniteMeasure Ω) (f : Ω → Ω') : MeasureTheory.FiniteMeasure Ω'
• MeasureTheory.FiniteMeasure.toMeasure_map 📋 Mathlib.MeasureTheory.Measure.FiniteMeasure
  {Ω : Type u_1} {Ω' : Type u_2} [MeasurableSpace Ω] [MeasurableSpace Ω'] (ν : MeasureTheory.FiniteMeasure Ω) (f : Ω → Ω') : ↑(ν.map f) = MeasureTheory.Measure.map f ↑ν
• MeasureTheory.FiniteMeasure.map.eq_1 📋 Mathlib.MeasureTheory.Measure.FiniteMeasure
  {Ω : Type u_1} {Ω' : Type u_2} [MeasurableSpace Ω] [MeasurableSpace Ω'] (ν : MeasureTheory.FiniteMeasure Ω) (f : Ω → Ω') : ν.map f = ⟨MeasureTheory.Measure.map f ↑ν, ⋯⟩
• MeasureTheory.FiniteMeasure.continuous_map 📋 Mathlib.MeasureTheory.Measure.FiniteMeasure
  {Ω : Type u_1} {Ω' : Type u_2} [MeasurableSpace Ω] [MeasurableSpace Ω'] [TopologicalSpace Ω] [OpensMeasurableSpace Ω] [TopologicalSpace Ω'] [BorelSpace Ω'] {f : Ω → Ω'} (f_cont : Continuous f) : Continuous fun ν => ν.map f
• MeasureTheory.FiniteMeasure.map_apply 📋 Mathlib.MeasureTheory.Measure.FiniteMeasure
  {Ω : Type u_1} {Ω' : Type u_2} [MeasurableSpace Ω] [MeasurableSpace Ω'] (ν : MeasureTheory.FiniteMeasure Ω) {f : Ω → Ω'} (f_mble : Measurable f) {A : Set Ω'} (A_mble : MeasurableSet A) : (ν.map f) A = ν (f ⁻¹' A)
• MeasureTheory.FiniteMeasure.map_apply_of_aemeasurable 📋 Mathlib.MeasureTheory.Measure.FiniteMeasure
  {Ω : Type u_1} {Ω' : Type u_2} [MeasurableSpace Ω] [MeasurableSpace Ω'] (ν : MeasureTheory.FiniteMeasure Ω) {f : Ω → Ω'} (f_aemble : AEMeasurable f ↑ν) {A : Set Ω'} (A_mble : MeasurableSet A) : (ν.map f) A = ν (f ⁻¹' A)
• MeasureTheory.FiniteMeasure.map_apply' 📋 Mathlib.MeasureTheory.Measure.FiniteMeasure
  {Ω : Type u_1} {Ω' : Type u_2} [MeasurableSpace Ω] [MeasurableSpace Ω'] (ν : MeasureTheory.FiniteMeasure Ω) {f : Ω → Ω'} (f_aemble : AEMeasurable f ↑ν) {A : Set Ω'} (A_mble : MeasurableSet A) : ↑(ν.map f) A = ↑ν (f ⁻¹' A)
• MeasureTheory.FiniteMeasure.map_add 📋 Mathlib.MeasureTheory.Measure.FiniteMeasure
  {Ω : Type u_1} {Ω' : Type u_2} [MeasurableSpace Ω] [MeasurableSpace Ω'] {f : Ω → Ω'} (f_mble : Measurable f) (ν₁ ν₂ : MeasureTheory.FiniteMeasure Ω) : (ν₁ + ν₂).map f = ν₁.map f + ν₂.map f
• MeasureTheory.FiniteMeasure.tendsto_map_of_tendsto_of_continuous 📋 Mathlib.MeasureTheory.Measure.FiniteMeasure
  {Ω : Type u_1} {Ω' : Type u_2} [MeasurableSpace Ω] [MeasurableSpace Ω'] [TopologicalSpace Ω] [OpensMeasurableSpace Ω] [TopologicalSpace Ω'] [BorelSpace Ω'] {ι : Type u_3} {L : Filter ι} (νs : ι → MeasureTheory.FiniteMeasure Ω) (ν : MeasureTheory.FiniteMeasure Ω) (lim : Filter.Tendsto νs L (nhds ν)) {f : Ω → Ω'} (f_cont : Continuous f) : Filter.Tendsto (fun i => (νs i).map f) L (nhds (ν.map f))
• MeasureTheory.FiniteMeasure.map_smul 📋 Mathlib.MeasureTheory.Measure.FiniteMeasure
  {Ω : Type u_1} {Ω' : Type u_2} [MeasurableSpace Ω] [MeasurableSpace Ω'] {f : Ω → Ω'} (c : NNReal) (ν : MeasureTheory.FiniteMeasure Ω) : (c • ν).map f = c • ν.map f
• MeasureTheory.FiniteMeasure.prod_swap 📋 Mathlib.MeasureTheory.Measure.FiniteMeasureProd
  {α : Type u_1} [MeasurableSpace α] {β : Type u_2} [MeasurableSpace β] (μ : MeasureTheory.FiniteMeasure α) (ν : MeasureTheory.FiniteMeasure β) : (μ.prod ν).map Prod.swap = ν.prod μ
• MeasureTheory.FiniteMeasure.map_prod_map 📋 Mathlib.MeasureTheory.Measure.FiniteMeasureProd
  {α : Type u_1} [MeasurableSpace α] {β : Type u_2} [MeasurableSpace β] (μ : MeasureTheory.FiniteMeasure α) (ν : MeasureTheory.FiniteMeasure β) {α' : Type u_3} [MeasurableSpace α'] {β' : Type u_4} [MeasurableSpace β'] {f : α → α'} {g : β → β'} (f_mble : Measurable f) (g_mble : Measurable g) : (μ.map f).prod (ν.map g) = (μ.prod ν).map (Prod.map f g)
• MeasureTheory.FiniteMeasure.map_fst_prod 📋 Mathlib.MeasureTheory.Measure.FiniteMeasureProd
  {α : Type u_1} [MeasurableSpace α] {β : Type u_2} [MeasurableSpace β] (μ : MeasureTheory.FiniteMeasure α) (ν : MeasureTheory.FiniteMeasure β) : (μ.prod ν).map Prod.fst = ν Set.univ • μ
• MeasureTheory.FiniteMeasure.map_snd_prod 📋 Mathlib.MeasureTheory.Measure.FiniteMeasureProd
  {α : Type u_1} [MeasurableSpace α] {β : Type u_2} [MeasurableSpace β] (μ : MeasureTheory.FiniteMeasure α) (ν : MeasureTheory.FiniteMeasure β) : (μ.prod ν).map Prod.snd = μ Set.univ • ν

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 bce1d65