Loogle!

Result

Found 487 definitions mentioning AEMeasurable. Of these, 10 have a name containing "MeasureTheory.Measure.Map".

• MeasureTheory.Measure.map_of_not_aemeasurable 📋 Mathlib.MeasureTheory.Measure.MeasureSpace
  {α : Type u_1} {β : Type u_2} {m0 : MeasurableSpace α} {mβ : MeasurableSpace β} {f : α → β} {μ : MeasureTheory.Measure α} (hf : ¬AEMeasurable f μ) : MeasureTheory.Measure.map f μ = 0
• MeasureTheory.Measure.map_eq_zero_iff 📋 Mathlib.MeasureTheory.Measure.MeasureSpace
  {α : Type u_1} {β : Type u_2} {m0 : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α} {f : α → β} (hf : AEMeasurable f μ) : MeasureTheory.Measure.map f μ = 0 ↔ μ = 0
• MeasureTheory.Measure.map_ne_zero_iff 📋 Mathlib.MeasureTheory.Measure.MeasureSpace
  {α : Type u_1} {β : Type u_2} {m0 : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α} {f : α → β} (hf : AEMeasurable f μ) : MeasureTheory.Measure.map f μ ≠ 0 ↔ μ ≠ 0
• MeasureTheory.Measure.map_apply_of_aemeasurable 📋 Mathlib.MeasureTheory.Measure.MeasureSpace
  {α : Type u_1} {β : Type u_2} {m0 : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α} {f : α → β} (hf : AEMeasurable f μ) {s : Set β} (hs : MeasurableSet s) : (MeasureTheory.Measure.map f μ) s = μ (f ⁻¹' s)
• MeasureTheory.Measure.map_apply₀ 📋 Mathlib.MeasureTheory.Measure.MeasureSpace
  {α : Type u_1} {β : Type u_2} {m0 : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α} {f : α → β} (hf : AEMeasurable f μ) {s : Set β} (hs : MeasureTheory.NullMeasurableSet s (MeasureTheory.Measure.map f μ)) : (MeasureTheory.Measure.map f μ) s = μ (f ⁻¹' s)
• MeasureTheory.Measure.map_def 📋 Mathlib.MeasureTheory.Measure.MeasureSpace
  {α : Type u_8} {β : Type u_9} [MeasurableSpace α] [MeasurableSpace β] (f : α → β) (μ : MeasureTheory.Measure α) : MeasureTheory.Measure.map f μ = if hf : AEMeasurable f μ then (MeasureTheory.Measure.mapₗ (AEMeasurable.mk f hf)) μ else 0
• MeasureTheory.Measure.map_toOuterMeasure 📋 Mathlib.MeasureTheory.Measure.MeasureSpace
  {α : Type u_1} {β : Type u_2} {m0 : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α} {f : α → β} (hf : AEMeasurable f μ) : (MeasureTheory.Measure.map f μ).toOuterMeasure = ((MeasureTheory.OuterMeasure.map f) μ.toOuterMeasure).trim
• MeasureTheory.Measure.mapₗ_mk_apply_of_aemeasurable 📋 Mathlib.MeasureTheory.Measure.MeasureSpace
  {α : Type u_1} {β : Type u_2} {m0 : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α} {f : α → β} (hf : AEMeasurable f μ) : (MeasureTheory.Measure.mapₗ (AEMeasurable.mk f hf)) μ = MeasureTheory.Measure.map f μ
• MeasureTheory.Measure.map_sum 📋 Mathlib.MeasureTheory.Measure.AEMeasurable
  {α : Type u_2} {β : Type u_3} {m0 : MeasurableSpace α} [MeasurableSpace β] {ι : Type u_7} {m : ι → MeasureTheory.Measure α} {f : α → β} (hf : AEMeasurable f (MeasureTheory.Measure.sum m)) : MeasureTheory.Measure.map f (MeasureTheory.Measure.sum m) = MeasureTheory.Measure.sum fun i => MeasureTheory.Measure.map f (m i)
• MeasureTheory.Measure.map_mono_of_aemeasurable 📋 Mathlib.MeasureTheory.Measure.AEMeasurable
  {α : Type u_2} {δ : Type u_5} {m0 : MeasurableSpace α} [MeasurableSpace δ] {μ ν : MeasureTheory.Measure α} {f : α → δ} (h : μ ≤ ν) (hf : AEMeasurable f ν) : MeasureTheory.Measure.map f μ ≤ MeasureTheory.Measure.map f 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, _ * _, _ ^ _, |- _ < _ → _
woould 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 4e1aab0 serving mathlib revision b513113