Loogle!

Result

Found 25 declarations mentioning HasSumUniformlyOn.

• HasSumUniformlyOn 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] (f : ι → β → α) (g : β → α) (s : Set β) [UniformSpace α] : Prop
• hasSumUniformlyOn_univ_iff 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} [UniformSpace α] : HasSumUniformlyOn f g Set.univ ↔ HasSumUniformly f g
• HasSumUniformly.hasSumUniformlyOn 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β} [UniformSpace α] (h : HasSumUniformly f g) : HasSumUniformlyOn f g s
• HasSumUniformlyOn.summableUniformlyOn 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β} [UniformSpace α] (h : HasSumUniformlyOn f g s) : SummableUniformlyOn f s
• SummableUniformlyOn.exists 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {s : Set β} [UniformSpace α] (h : SummableUniformlyOn f s) : ∃ g, HasSumUniformlyOn f g s
• HasSumUniformlyOn.hasSumLocallyUniformlyOn 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β} [UniformSpace α] [TopologicalSpace β] (h : HasSumUniformlyOn f g s) : HasSumLocallyUniformlyOn f g s
• HasSumUniformlyOn.congr_right 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β} [UniformSpace α] {g' : β → α} (h : HasSumUniformlyOn f g s) (hgg' : Set.EqOn g g' s) : HasSumUniformlyOn f g' s
• hasSumLocallyUniformly_of_forall_compact 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} [UniformSpace α] [TopologicalSpace β] [LocallyCompactSpace β] (h : ∀ (K : Set β), IsCompact K → HasSumUniformlyOn f g K) : HasSumLocallyUniformly f g
• HasSumUniformlyOn.mono 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β} [UniformSpace α] {t : Set β} (h : HasSumUniformlyOn f g t) (hst : s ⊆ t) : HasSumUniformlyOn f g s
• SummableUniformlyOn.hasSumUniformlyOn 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {s : Set β} [UniformSpace α] (h : SummableUniformlyOn f s) : HasSumUniformlyOn f (fun x => ∑' (i : ι), f i x) s
• summableUniformlyOn_iff_hasSumUniformlyOn 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {s : Set β} [UniformSpace α] : SummableUniformlyOn f s ↔ HasSumUniformlyOn f (fun x => ∑' (i : ι), f i x) s
• HasSumUniformlyOn.tendstoUniformlyOn_finsetRange 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} [AddCommMonoid α] {g : β → α} {s : Set β} [UniformSpace α] {f : ℕ → β → α} (h : HasSumUniformlyOn f g s) : TendstoUniformlyOn (fun x1 x2 => ∑ i ∈ Finset.range x1, f i x2) g Filter.atTop s
• HasSumUniformlyOn.hasSum 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {x : β} {s : Set β} [UniformSpace α] (h : HasSumUniformlyOn f g s) (hx : x ∈ s) : HasSum (fun x_1 => f x_1 x) (g x)
• HasSumUniformlyOn.tsum_eq 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β} [UniformSpace α] [T2Space α] (h : HasSumUniformlyOn f g s) : Set.EqOn (fun x => ∑' (b : ι), f b x) g s
• HasSumUniformlyOn.tsum_eqOn 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β} [UniformSpace α] [T2Space α] (h : HasSumUniformlyOn f g s) : Set.EqOn (fun x => ∑' (b : ι), f b x) g s
• hasSumLocallyUniformly_of_of_forall_exists_nhds 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} [UniformSpace α] [TopologicalSpace β] (h : ∀ (x : β), ∃ t ∈ nhds x, HasSumUniformlyOn f g t) : HasSumLocallyUniformly f g
• HasSumUniformlyOn.tendstoUniformlyOn 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β} [UniformSpace α] : HasSumUniformlyOn f g s → TendstoUniformlyOn (fun x1 x2 => ∑ i ∈ x1, f i x2) g Filter.atTop s
• hasSumUniformlyOn_iff_tendstoUniformlyOn 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β} [UniformSpace α] : HasSumUniformlyOn f g s ↔ TendstoUniformlyOn (fun x1 x2 => ∑ i ∈ x1, f i x2) g Filter.atTop s
• hasSumLocallyUniformlyOn_of_forall_compact 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β} [UniformSpace α] [TopologicalSpace β] (hs : IsOpen s) [LocallyCompactSpace β] (h : ∀ K ⊆ s, IsCompact K → HasSumUniformlyOn f g K) : HasSumLocallyUniformlyOn f g s
• hasSumLocallyUniformlyOn_of_of_forall_exists_nhds 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β} [UniformSpace α] [TopologicalSpace β] (h : ∀ x ∈ s, ∃ t ∈ nhdsWithin x s, HasSumUniformlyOn f g t) : HasSumLocallyUniformlyOn f g s
• HasSumUniformlyOn.congr 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] {f : ι → β → α} {g : β → α} {s : Set β} [UniformSpace α] {f' : ι → β → α} (h : HasSumUniformlyOn f g s) (hff' : ∀ᶠ (n : Finset ι) in Filter.atTop, Set.EqOn (fun x => ∑ i ∈ n, f i x) (fun x => ∑ i ∈ n, f' i x) s) : HasSumUniformlyOn f' g s
• HasSumUniformlyOn.eq_1 📋 Mathlib.Topology.Algebra.InfiniteSum.UniformOn
  {α : Type u_1} {β : Type u_2} {ι : Type u_3} [AddCommMonoid α] (f : ι → β → α) (g : β → α) (s : Set β) [UniformSpace α] : HasSumUniformlyOn f g s = HasSum (⇑(UniformOnFun.ofFun {s}) ∘ f) ((UniformOnFun.ofFun {s}) g)
• Summable.hasSumUniformlyOn_log_one_add 📋 Mathlib.Analysis.Normed.Module.MultipliableUniformlyOn
  {α : Type u_1} {ι : Type u_2} {K : Set α} {u : ι → ℝ} {f : ι → α → ℂ} (hu : Summable u) (h : ∀ᶠ (i : ι) in Filter.cofinite, ∀ x ∈ K, ‖f i x‖ ≤ u i) : HasSumUniformlyOn (fun i x => Complex.log (1 + f i x)) (fun x => ∑' (i : ι), Complex.log (1 + f i x)) K
• HasSumUniformlyOn.of_norm_le_summable 📋 Mathlib.Topology.Algebra.InfiniteSum.TsumUniformlyOn
  {α : Type u_1} {β : Type u_2} {F : Type u_3} [NormedAddCommGroup F] [CompleteSpace F] {u : α → ℝ} {f : α → β → F} (hu : Summable u) {s : Set β} (hfu : ∀ (n : α), ∀ x ∈ s, ‖f n x‖ ≤ u n) : HasSumUniformlyOn f (fun x => ∑' (n : α), f n x) s
• HasSumUniformlyOn.of_norm_le_summable_eventually 📋 Mathlib.Topology.Algebra.InfiniteSum.TsumUniformlyOn
  {β : Type u_2} {F : Type u_3} [NormedAddCommGroup F] [CompleteSpace F] {ι : Type u_4} {f : ι → β → F} {u : ι → ℝ} (hu : Summable u) {s : Set β} (hfu : ∀ᶠ (n : ι) in Filter.cofinite, ∀ x ∈ s, ‖f n x‖ ≤ u n) : HasSumUniformlyOn f (fun x => ∑' (n : ι), f n x) s

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 6ff4759 serving mathlib revision 6ec3a4c