Loogle!

Result

Found 11 declarations mentioning MeasureTheory.VectorMeasure.map.

• MeasureTheory.VectorMeasure.map 📋 Mathlib.MeasureTheory.VectorMeasure.Basic
  {α : Type u_1} {β : Type u_2} [MeasurableSpace α] [MeasurableSpace β] {M : Type u_3} [AddCommMonoid M] [TopologicalSpace M] (v : MeasureTheory.VectorMeasure α M) (f : α → β) : MeasureTheory.VectorMeasure β M
• MeasureTheory.VectorMeasure.map_id 📋 Mathlib.MeasureTheory.VectorMeasure.Basic
  {α : Type u_1} [MeasurableSpace α] {M : Type u_3} [AddCommMonoid M] [TopologicalSpace M] (v : MeasureTheory.VectorMeasure α M) : v.map id = v
• MeasureTheory.VectorMeasure.map_apply 📋 Mathlib.MeasureTheory.VectorMeasure.Basic
  {α : Type u_1} {β : Type u_2} [MeasurableSpace α] [MeasurableSpace β] {M : Type u_3} [AddCommMonoid M] [TopologicalSpace M] (v : MeasureTheory.VectorMeasure α M) {f : α → β} (hf : Measurable f) {s : Set β} (hs : MeasurableSet s) : ↑(v.map f) s = ↑v (f ⁻¹' s)
• MeasureTheory.VectorMeasure.map_not_measurable 📋 Mathlib.MeasureTheory.VectorMeasure.Basic
  {α : Type u_1} {β : Type u_2} [MeasurableSpace α] [MeasurableSpace β] {M : Type u_3} [AddCommMonoid M] [TopologicalSpace M] (v : MeasureTheory.VectorMeasure α M) {f : α → β} (hf : ¬Measurable f) : v.map f = 0
• MeasureTheory.VectorMeasure.map_zero 📋 Mathlib.MeasureTheory.VectorMeasure.Basic
  {α : Type u_1} {β : Type u_2} [MeasurableSpace α] [MeasurableSpace β] {M : Type u_3} [AddCommMonoid M] [TopologicalSpace M] (f : α → β) : MeasureTheory.VectorMeasure.map 0 f = 0
• MeasureTheory.VectorMeasure.AbsolutelyContinuous.map 📋 Mathlib.MeasureTheory.VectorMeasure.Basic
  {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {M : Type u_4} {N : Type u_5} [AddCommMonoid M] [TopologicalSpace M] [AddCommMonoid N] [TopologicalSpace N] {v : MeasureTheory.VectorMeasure α M} {w : MeasureTheory.VectorMeasure α N} [MeasureTheory.MeasureSpace β] (h : v.AbsolutelyContinuous w) (f : α → β) : (v.map f).AbsolutelyContinuous (w.map f)
• MeasureTheory.VectorMeasure.map_add 📋 Mathlib.MeasureTheory.VectorMeasure.Basic
  {α : Type u_1} {β : Type u_2} [MeasurableSpace α] [MeasurableSpace β] {M : Type u_3} [AddCommMonoid M] [TopologicalSpace M] [ContinuousAdd M] (v w : MeasureTheory.VectorMeasure α M) (f : α → β) : (v + w).map f = v.map f + w.map f
• MeasureTheory.VectorMeasure.map_smul 📋 Mathlib.MeasureTheory.VectorMeasure.Basic
  {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} [MeasurableSpace β] {M : Type u_3} [AddCommMonoid M] [TopologicalSpace M] {R : Type u_4} [Semiring R] [DistribMulAction R M] [ContinuousConstSMul R M] {v : MeasureTheory.VectorMeasure α M} {f : α → β} (c : R) : (c • v).map f = c • v.map f
• MeasureTheory.VectorMeasure.map.eq_1 📋 Mathlib.MeasureTheory.VectorMeasure.Basic
  {α : Type u_1} {β : Type u_2} [MeasurableSpace α] [MeasurableSpace β] {M : Type u_3} [AddCommMonoid M] [TopologicalSpace M] (v : MeasureTheory.VectorMeasure α M) (f : α → β) : v.map f = if hf : Measurable f then { measureOf' := fun s => if MeasurableSet s then ↑v (f ⁻¹' s) else 0, empty' := ⋯, not_measurable' := ⋯, m_iUnion' := ⋯ } else 0
• MeasureTheory.VectorMeasure.mapGm_apply 📋 Mathlib.MeasureTheory.VectorMeasure.Basic
  {α : Type u_1} {β : Type u_2} [MeasurableSpace α] [MeasurableSpace β] {M : Type u_3} [AddCommMonoid M] [TopologicalSpace M] [ContinuousAdd M] (f : α → β) (v : MeasureTheory.VectorMeasure α M) : (MeasureTheory.VectorMeasure.mapGm f) v = v.map f
• MeasureTheory.VectorMeasure.mapₗ_apply 📋 Mathlib.MeasureTheory.VectorMeasure.Basic
  {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} [MeasurableSpace β] {M : Type u_3} [AddCommMonoid M] [TopologicalSpace M] {R : Type u_4} [Semiring R] [Module R M] [ContinuousConstSMul R M] [ContinuousAdd M] (f : α → β) (v : MeasureTheory.VectorMeasure α M) : (MeasureTheory.VectorMeasure.mapₗ f) v = v.map f

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