Theorems · Theorem · sequences and series

summable_abs_iff

∀ {ι : Type u_1} {α : Type u_3} [inst : AddCommGroup α] [inst_1 : LinearOrder α] [IsOrderedAddMonoid α]
  [inst_3 : UniformSpace α] [IsUniformAddGroup α] [CompleteSpace α] {f : ι → α}, (Summable fun x => |f x|) ↔ Summable f

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Order

Cited by

3 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupLinearOrderIsOrderedAddMonoidUniformSpaceIsUniformAddGroupCompleteSpace