Loogle!

Result

Found 15 declarations mentioning MeasureTheory.Measure.euclideanHausdorffMeasure.

• MeasureTheory.Measure.euclideanHausdorffMeasure 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {X : Type u_1} [EMetricSpace X] [MeasurableSpace X] [BorelSpace X] (d : ℕ) : MeasureTheory.Measure X
• instIsAddLeftInvariantEuclideanHausdorffMeasureOfIsIsometricVAdd 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {X : Type u_1} [EMetricSpace X] [MeasurableSpace X] [BorelSpace X] [AddGroup X] [IsIsometricVAdd X X] (d : ℕ) : (MeasureTheory.Measure.euclideanHausdorffMeasure d).IsAddLeftInvariant
• Isometry.map_euclideanHausdorffMeasure 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {X : Type u_1} {Y : Type u_2} [EMetricSpace X] [MeasurableSpace X] [BorelSpace X] [EMetricSpace Y] [MeasurableSpace Y] [BorelSpace Y] {f : X → Y} {d : ℕ} (hf : Isometry f) : MeasureTheory.Measure.map f (MeasureTheory.Measure.euclideanHausdorffMeasure d) = (MeasureTheory.Measure.euclideanHausdorffMeasure d).restrict (Set.range f)
• instIsAddRightInvariantEuclideanHausdorffMeasureOfIsIsometricVAddAddOpposite 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {X : Type u_1} [EMetricSpace X] [MeasurableSpace X] [BorelSpace X] [AddGroup X] [IsIsometricVAdd Xᵃᵒᵖ X] (d : ℕ) : (MeasureTheory.Measure.euclideanHausdorffMeasure d).IsAddRightInvariant
• instVAddInvariantMeasureEuclideanHausdorffMeasureOfIsIsometricVAdd 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {X : Type u_1} [EMetricSpace X] [MeasurableSpace X] [BorelSpace X] {α : Type u_5} [AddGroup α] [AddAction α X] [IsIsometricVAdd α X] (d : ℕ) : MeasureTheory.VAddInvariantMeasure α X (MeasureTheory.Measure.euclideanHausdorffMeasure d)
• Isometry.euclideanHausdorffMeasure_image 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {X : Type u_1} {Y : Type u_2} [EMetricSpace X] [MeasurableSpace X] [BorelSpace X] [EMetricSpace Y] [MeasurableSpace Y] [BorelSpace Y] {f : X → Y} {d : ℕ} (hf : Isometry f) (s : Set X) : (MeasureTheory.Measure.euclideanHausdorffMeasure d) (f '' s) = (MeasureTheory.Measure.euclideanHausdorffMeasure d) s
• IsometryEquiv.measurePreserving_euclideanHausdorffMeasure 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {X : Type u_1} {Y : Type u_2} [EMetricSpace X] [MeasurableSpace X] [BorelSpace X] [EMetricSpace Y] [MeasurableSpace Y] [BorelSpace Y] (e : X ≃ᵢ Y) (d : ℕ) : MeasureTheory.MeasurePreserving (⇑e) (MeasureTheory.Measure.euclideanHausdorffMeasure d) (MeasureTheory.Measure.euclideanHausdorffMeasure d)
• Isometry.euclideanHausdorffMeasure_preimage 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {X : Type u_1} {Y : Type u_2} [EMetricSpace X] [MeasurableSpace X] [BorelSpace X] [EMetricSpace Y] [MeasurableSpace Y] [BorelSpace Y] {f : X → Y} {d : ℕ} (hf : Isometry f) (s : Set Y) : (MeasureTheory.Measure.euclideanHausdorffMeasure d) (f ⁻¹' s) = (MeasureTheory.Measure.euclideanHausdorffMeasure d) (s ∩ Set.range f)
• InnerProductSpace.euclideanHausdorffMeasure_eq_volume 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {V : Type u_3} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MeasurableSpace V] [BorelSpace V] [FiniteDimensional ℝ V] : MeasureTheory.Measure.euclideanHausdorffMeasure (Module.finrank ℝ V) = MeasureTheory.volume
• EuclideanGeometry.measurePreserving_vaddConst 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {V : Type u_3} {P : Type u_4} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MeasurableSpace V] [BorelSpace V] [FiniteDimensional ℝ V] [MetricSpace P] [MeasurableSpace P] [BorelSpace P] [NormedAddTorsor V P] (p : P) : MeasureTheory.MeasurePreserving (⇑(IsometryEquiv.vaddConst p)) MeasureTheory.volume (MeasureTheory.Measure.euclideanHausdorffMeasure (Module.finrank ℝ V))
• EuclideanGeometry.euclideanHausdorffMeasure_eq 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {V : Type u_3} {P : Type u_4} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MeasurableSpace V] [BorelSpace V] [FiniteDimensional ℝ V] [MetricSpace P] [MeasurableSpace P] [BorelSpace P] [NormedAddTorsor V P] (p : P) : MeasureTheory.Measure.euclideanHausdorffMeasure (Module.finrank ℝ V) = MeasureTheory.Measure.map (⇑(IsometryEquiv.vaddConst p)) MeasureTheory.volume
• EuclideanSpace.euclideanHausdorffMeasure_eq_volume 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  (d : ℕ) : MeasureTheory.Measure.euclideanHausdorffMeasure d = MeasureTheory.volume
• MeasureTheory.Measure.euclideanHausdorffMeasure_smul₀ 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {𝕜 : Type u_3} {E : Type u_4} [NormedAddCommGroup E] [NormedDivisionRing 𝕜] [Module 𝕜 E] [NormSMulClass 𝕜 E] [MeasurableSpace E] [BorelSpace E] (d : ℕ) {r : 𝕜} (hr : r ≠ 0) (s : Set E) : (MeasureTheory.Measure.euclideanHausdorffMeasure d) (r • s) = ‖r‖₊ ^ d • (MeasureTheory.Measure.euclideanHausdorffMeasure d) s
• AffineSubspace.euclideanHausdorffMeasure_coe_image 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {V : Type u_3} {P : Type u_4} [NormedAddCommGroup V] [InnerProductSpace ℝ V] [MetricSpace P] [MeasurableSpace P] [BorelSpace P] [NormedAddTorsor V P] (d : ℕ) (s : AffineSubspace ℝ P) (t : Set ↥s) : (MeasureTheory.Measure.euclideanHausdorffMeasure d) (Subtype.val '' t) = (MeasureTheory.Measure.euclideanHausdorffMeasure d) t
• MeasureTheory.Measure.euclideanHausdorffMeasure_def 📋 Mathlib.Geometry.Euclidean.Volume.Measure
  {X : Type u_1} [EMetricSpace X] [MeasurableSpace X] [BorelSpace X] (d : ℕ) : MeasureTheory.Measure.euclideanHausdorffMeasure d = MeasureTheory.volume.addHaarScalarFactor (MeasureTheory.Measure.hausdorffMeasure ↑d) • MeasureTheory.Measure.hausdorffMeasure ↑d

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.

5. You can filter for definitions vs theorems: Using ⊢ (_ : Type _) finds all definitions which provide data while ⊢ (_ : Prop) finds all theorems (and definitions of proofs).

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 128218b serving mathlib revision 9b12c6a