Theorems · Theorem · sequences and series

Summable.tsum_pos

∀ {ι : Type u_1} {α : Type u_3} {L : SummationFilter ι} [inst : AddCommGroup α] [inst_1 : PartialOrder α]
  [IsOrderedAddMonoid α] [inst_3 : TopologicalSpace α] [IsTopologicalAddGroup α] [OrderClosedTopology α] {g : ι → α}
  [L.LeAtTop] [L.NeBot], Summable g L → (∀ (i : ι), 0 ≤ g i) → ∀ (i : ι), 0 < g i → 0 < ∑'[L] (i : ι), g i

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

3 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupPartialOrderIsOrderedAddMonoidTopologicalSpaceIsTopologicalAddGroupOrderClosedTopologySummationFilter.LeAtTopSummationFilter.NeBot