@@ -3056,7 +3056,7 @@ theorem Tendsto.not_tendsto {f : α → β} {a : Filter α} {b₁ b₂ : Filter
3056
3056
(tendsto_inf.2 ⟨hf, hf'⟩).neBot.ne hb.eq_bot
3057
3057
#align filter.tendsto.not_tendsto Filter.Tendsto.not_tendsto
3058
3058
3059
- theorem Tendsto.if {l₁ : Filter α} {l₂ : Filter β} {f g : α → β} {p : α → Prop }
3059
+ protected theorem Tendsto.if {l₁ : Filter α} {l₂ : Filter β} {f g : α → β} {p : α → Prop }
3060
3060
[∀ x, Decidable (p x)] (h₀ : Tendsto f (l₁ ⊓ 𝓟 { x | p x }) l₂)
3061
3061
(h₁ : Tendsto g (l₁ ⊓ 𝓟 { x | ¬p x }) l₂) :
3062
3062
Tendsto (fun x => if p x then f x else g x) l₁ l₂ := by
@@ -3068,13 +3068,13 @@ theorem Tendsto.if {l₁ : Filter α} {l₂ : Filter β} {f g : α → β} {p :
3068
3068
exacts [hp₀ h, hp₁ h]
3069
3069
#align filter.tendsto.if Filter.Tendsto.if
3070
3070
3071
- theorem Tendsto.if' {α β : Type _} {l₁ : Filter α} {l₂ : Filter β} {f g : α → β} {p : α → Prop }
3072
- [DecidablePred p] (hf : Tendsto f l₁ l₂) (hg : Tendsto g l₁ l₂) :
3071
+ protected theorem Tendsto.if' {α β : Type _} {l₁ : Filter α} {l₂ : Filter β} {f g : α → β}
3072
+ {p : α → Prop } [DecidablePred p] (hf : Tendsto f l₁ l₂) (hg : Tendsto g l₁ l₂) :
3073
3073
Tendsto (fun a => if p a then f a else g a) l₁ l₂ :=
3074
3074
(tendsto_inf_left hf).if (tendsto_inf_left hg)
3075
3075
#align filter.tendsto.if' Filter.Tendsto.if'
3076
3076
3077
- theorem Tendsto.piecewise {l₁ : Filter α} {l₂ : Filter β} {f g : α → β} {s : Set α}
3077
+ protected theorem Tendsto.piecewise {l₁ : Filter α} {l₂ : Filter β} {f g : α → β} {s : Set α}
3078
3078
[∀ x, Decidable (x ∈ s)] (h₀ : Tendsto f (l₁ ⊓ 𝓟 s) l₂) (h₁ : Tendsto g (l₁ ⊓ 𝓟 (sᶜ)) l₂) :
3079
3079
Tendsto (piecewise s f g) l₁ l₂ :=
3080
3080
Tendsto.if h₀ h₁
0 commit comments