@[instance]
Equations
theorem
nnreal.tendsto_coe
{α : Type u_1}
{f : filter α}
{m : α → ℝ≥0}
{x : ℝ≥0} :
filter.tendsto (λ (a : α), ↑(m a)) f (𝓝 ↑x) ↔ filter.tendsto m f (𝓝 x)
theorem
nnreal.tendsto_of_real
{α : Type u_1}
{f : filter α}
{m : α → ℝ}
{x : ℝ}
(h : filter.tendsto m f (𝓝 x)) :
filter.tendsto (λ (a : α), nnreal.of_real (m a)) f (𝓝 (nnreal.of_real x))
theorem
nnreal.tendsto.sub
{α : Type u_1}
{f : filter α}
{m n : α → ℝ≥0}
{r p : ℝ≥0}
(hm : filter.tendsto m f (𝓝 r))
(hn : filter.tendsto n f (𝓝 p)) :
filter.tendsto (λ (a : α), m a - n a) f (𝓝 (r - p))
theorem
nnreal.continuous.sub
{α : Type u_1}
[topological_space α]
{f g : α → ℝ≥0}
(hf : continuous f)
(hg : continuous g) :
continuous (λ (a : α), f a - g a)
theorem
nnreal.summable_comp_injective
{α : Type u_1}
{β : Type u_2}
{f : α → ℝ≥0}
(hf : summable f)
{i : β → α}
(hi : function.injective i) :