Theorems · Theorem · sequences and series

SemiconjBy.tsum_right

∀ {ι : Type u_1} {α : Type u_3} {L : SummationFilter ι} [inst : NonUnitalNonAssocSemiring α]
  [inst_1 : TopologicalSpace α] [IsTopologicalSemiring α] [T2Space α] [L.NeBot] {f g : ι → α} (a : α),
  Summable f L →
    Summable g L → (∀ (i : ι), SemiconjBy a (f i) (g i)) → SemiconjBy a (∑'[L] (i : ι), f i) (∑'[L] (i : ι), g i)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Ring

Cited by

1 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NonUnitalNonAssocSemiringTopologicalSpaceIsTopologicalSemiringT2SpaceSummationFilter.NeBot