Theorems · Definition · sequences and series

tprod

{α : Type u_4} →
  {β : Type u_5} →
    [CommMonoid α] → [TopologicalSpace α] → (β → α) → optParam (SummationFilter β) (SummationFilter.unconditional β) → α

∏' i, f i is the unconditional product of f, if it exists, or 1 otherwise. More generally, if L is a SummationFilter, ∏'[L] i, f i is the product of f with respect to L if it exists, and 1 otherwise. (Note that even if the unconditional product exists, it might not be unique if the topology is not separated. When the multiplicative support of f is finite, we make the most reasonable choice, to use the product over the multiplicative support. Otherwise, we choose arbitrarily an a satisfying HasProd f a. Similar remarks apply to more general summation filters.)

Defined in

Mathlib.Topology.Algebra.InfiniteSum.Defs

Cited by

230 results in Mathlib

Foundations

Depth 74 from the axioms, rests on 1,109 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidTopologicalSpace