Theorems · Theorem · functional analysis

GeneralSchauderBasis.tendsto_proj

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {X : Type u_2} [inst_1 : NormedAddCommGroup X]
  [inst_2 : NormedSpace 𝕜 X] {β : Type u_3} {L : SummationFilter β} (b : GeneralSchauderBasis β 𝕜 X L) (x : X),
  Filter.Tendsto (fun A => (b.proj A) x) L.filter (nhds x)

The projections b.proj A x converge to x along the summation filter.

Defined in

Mathlib.Analysis.Normed.Module.Bases

Cited by

1 results in Mathlib

Foundations

Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace