Theorems · Theorem · sequences and series

hasSum_zero_iff_of_nonneg

∀ {ι : Type u_4} {α : Type u_5} {L : SummationFilter ι} [inst : AddCommMonoid α] [inst_1 : PartialOrder α]
  [IsOrderedAddMonoid α] [inst_3 : TopologicalSpace α] [OrderClosedTopology α] {f : ι → α} [L.LeAtTop] [L.NeBot],
  (∀ (i : ι), 0 ≤ f i) → (HasSum f 0 L ↔ f = 0)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

2 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidPartialOrderIsOrderedAddMonoidTopologicalSpaceOrderClosedTopologySummationFilter.LeAtTopSummationFilter.NeBot