case intro
α : Type u_2
ι : Type u_1
E : Type u_3
m : MeasurableSpace α
μ : Measure α
inst✝² : MetricSpace E
f✝ : ℕ → α → E
g✝ : α → E
u : Filter ι
inst✝¹ : NeBot u
inst✝ : IsCountablyGenerated u
f : ι → α → E
g : α → E
hfg : TendstoInMeasure μ f u g
ms : ℕ → ι
hms : TendstoInMeasure μ (fun n => f (ms n)) atTop g
⊢ ∃ ns, ∀ᵐ (x : α) ∂μ, Tendsto (fun i => f (ns i) x) atTop (𝓝 (g x))
α : Type u_2
ι : Type u_1
E : Type u_3
m : MeasurableSpace α
μ : Measure α
inst✝² : MetricSpace E
f✝ : ℕ → α → E
g✝ : α → E
u : Filter ι
inst✝¹ : NeBot u
inst✝ : IsCountablyGenerated u
f : ι → α → E
g : α → E
hfg : TendstoInMeasure μ f u g
⊢ ∃ ns, ∀ᵐ (x : α) ∂μ, Tendsto (fun i => f (ns i) x) atTop (𝓝 (g x))
obtain ⟨ms, hms⟩ := hfg.exists_seq_tendstoInMeasure_atTop
case intro.intro.intro
α : Type u_2
ι : Type u_1
E : Type u_3
m : MeasurableSpace α
μ : Measure α
inst✝² : MetricSpace E
f✝ : ℕ → α → E
g✝ : α → E
u : Filter ι
inst✝¹ : NeBot u
inst✝ : IsCountablyGenerated u
f : ι → α → E
g : α → E
hfg : TendstoInMeasure μ f u g
ms : ℕ → ι
hms : TendstoInMeasure μ (fun n => f (ms n)) atTop g
ns : ℕ → ℕ
hns : ∀ᵐ (x : α) ∂μ, Tendsto (fun i => f (ms (ns i)) x) atTop (𝓝 (g x))
⊢ ∃ ns, ∀ᵐ (x : α) ∂μ, Tendsto (fun i => f (ns i) x) atTop (𝓝 (g x))
case intro
α : Type u_2
ι : Type u_1
E : Type u_3
m : MeasurableSpace α
μ : Measure α
inst✝² : MetricSpace E
f✝ : ℕ → α → E
g✝ : α → E
u : Filter ι
inst✝¹ : NeBot u
inst✝ : IsCountablyGenerated u
f : ι → α → E
g : α → E
hfg : TendstoInMeasure μ f u g
ms : ℕ → ι
hms : TendstoInMeasure μ (fun n => f (ms n)) atTop g
⊢ ∃ ns, ∀ᵐ (x : α) ∂μ, Tendsto (fun i => f (ns i) x) atTop (𝓝 (g x))
obtain ⟨ns, -, hns⟩ := hms.exists_seq_tendsto_ae
no goals
case intro.intro.intro
α : Type u_2
ι : Type u_1
E : Type u_3
m : MeasurableSpace α
μ : Measure α
inst✝² : MetricSpace E
f✝ : ℕ → α → E
g✝ : α → E
u : Filter ι
inst✝¹ : NeBot u
inst✝ : IsCountablyGenerated u
f : ι → α → E
g : α → E
hfg : TendstoInMeasure μ f u g
ms : ℕ → ι
hms : TendstoInMeasure μ (fun n => f (ms n)) atTop g
ns : ℕ → ℕ
hns : ∀ᵐ (x : α) ∂μ, Tendsto (fun i => f (ms (ns i)) x) atTop (𝓝 (g x))
⊢ ∃ ns, ∀ᵐ (x : α) ∂μ, Tendsto (fun i => f (ns i) x) atTop (𝓝 (g x))
exact ⟨ms ∘ ns, hns⟩