Theorems · Theorem · sequences and series

Summable.tsum_eq_zero_iff

∀ {ι : Type u_1} {α : Type u_3} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α]
  [CanonicallyOrderedAdd α] [inst_4 : TopologicalSpace α] [OrderClosedTopology α] {f : ι → α},
  Summable f → (∑' (i : ι), f i = 0 ↔ ∀ (x : ι), f x = 0)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

4 results in Mathlib

Foundations

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

Assumes

AddCommMonoidPartialOrderIsOrderedAddMonoidCanonicallyOrderedAddTopologicalSpaceOrderClosedTopology