mathlib documentation

topology.​instances.​nnreal

topology.​instances.​nnreal

theorem nnreal.​tendsto_coe {α : Type u_1} {f : filter α} {m : α → nnreal} {x : nnreal} :
filter.tendsto (λ (a : α), (m a)) f (nhds x) filter.tendsto m f (nhds x)

theorem nnreal.​tendsto_of_real {α : Type u_1} {f : filter α} {m : α → } {x : } :
filter.tendsto m f (nhds x)filter.tendsto (λ (a : α), nnreal.of_real (m a)) f (nhds (nnreal.of_real x))

theorem nnreal.​tendsto.​sub {α : Type u_1} {f : filter α} {m n : α → nnreal} {r p : nnreal} :
filter.tendsto m f (nhds r)filter.tendsto n f (nhds p)filter.tendsto (λ (a : α), m a - n a) f (nhds (r - p))

theorem nnreal.​continuous.​sub {α : Type u_1} [topological_space α] {f g : α → nnreal} :
continuous fcontinuous gcontinuous (λ (a : α), f a - g a)

theorem nnreal.​has_sum_coe {α : Type u_1} {f : α → nnreal} {r : nnreal} :
has_sum (λ (a : α), (f a)) r has_sum f r

theorem nnreal.​summable_coe {α : Type u_1} {f : α → nnreal} :
summable (λ (a : α), (f a)) summable f

theorem nnreal.​coe_tsum {α : Type u_1} {f : α → nnreal} :
(∑' (a : α), f a) = ∑' (a : α), (f a)

theorem nnreal.​summable_comp_injective {α : Type u_1} {β : Type u_2} {f : α → nnreal} (hf : summable f) {i : β → α} :