Theorems · Theorem · sequences and series

lt_hasSum

∀ {ι : Type u_1} {α : Type u_3} {L : SummationFilter ι} [inst : AddCommMonoid α] [inst_1 : Preorder α]
  [IsOrderedAddMonoid α] [inst_3 : TopologicalSpace α] [OrderClosedTopology α] {f : ι → α} {a : α} [L.NeBot] [L.LeAtTop]
  [AddRightStrictMono α], HasSum f a L → ∀ (i : ι), (∀ (j : ι), j ≠ i → 0 ≤ f j) → ∀ (j : ι), j ≠ i → 0 < f j → f i < a

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidPreorderIsOrderedAddMonoidTopologicalSpaceOrderClosedTopologySummationFilter.NeBotSummationFilter.LeAtTopAddRightStrictMono