Theorems · Theorem · functional analysis
SeminormedGroup.tendstoUniformlyOn_one
∀ {ι : Type u_2} {κ : Type u_3} {G : Type u_6} [inst : SeminormedGroup G] {f : ι → κ → G} {s : Set κ} {l : Filter ι},
TendstoUniformlyOn f 1 l s ↔ ∀ ε > 0, ∀ᶠ (i : ι) in l, ∀ x ∈ s, ‖f i x‖ < ε- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedGroup
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- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Filterstatement and proof · cited by 8,121
- Norm.normstatement and proof · cited by 5,413
- Filter.Eventuallystatement and proof · cited by 3,134
- SeminormedGroupstatement and proof · cited by 250
- TendstoUniformlyOnstatement · cited by 129
- dist_one_leftproof · cited by 6
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