Theorems · Theorem · functional analysis
Filter.Tendsto.nnnorm
∀ {α : Type u_1} {E : Type u_4} [inst : SeminormedAddGroup E] {a : E} {l : Filter α} {f : α → E},
Filter.Tendsto f l (nhds a) → Filter.Tendsto (fun x => ‖f x‖₊) l (nhds ‖a‖₊)- Defined in
- Mathlib.Analysis.Normed.Group.Continuity
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedAddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- NNRealstatement · cited by 4,310
- Filter.Tendstostatement and proof · cited by 3,814
- NNNorm.nnnormstatement · cited by 952
- Filter.Tendsto.compproof · cited by 560
- SeminormedAddGroupstatement and proof · cited by 331
- Continuous.continuousAtproof · cited by 297
- continuous_nnnormproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.SimpleFunc.tendsto_approxOn_Lp_eLpNormproof · cited by 3
- ContinuousWithinAt.nnnormproof · cited by 2
- ContinuousAt.nnnormproof · cited by 1