Theorems · Theorem · functional analysis

ContinuousLinearMap.hasSum

∀ {ι : Type u_5} {R : Type u_7} {R₂ : Type u_8} {M : Type u_9} {M₂ : Type u_10} [inst : Semiring R]
  [inst_1 : Semiring R₂] [inst_2 : AddCommMonoid M] [inst_3 : Module R M] [inst_4 : AddCommMonoid M₂]
  [inst_5 : Module R₂ M₂] [inst_6 : TopologicalSpace M] [inst_7 : TopologicalSpace M₂] {σ : R →+* R₂}
  {L : SummationFilter ι} {f : ι → M} (φ : M →SL[σ] M₂) {x : M}, HasSum f x L → HasSum (fun b => φ (f b)) (φ x) L

Applying a continuous linear map commutes with taking an (infinite) sum.

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Module

Cited by

13 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidModuleAddCommMonoidModuleTopologicalSpaceTopologicalSpace